Document Zbl 1218.33021

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1218.33021 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1218.33021?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1218.33021" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/haubold.hans-joachim" title="Author Profile">Haubold, H. J.</a>; <a href="/authors/mathai.arak-mathai" title="Author Profile">Mathai, A. M.</a>; <a href="/authors/saxena.ram-kishore" title="Author Profile">Saxena, R. K.</a></div> <h2 class="title"> <strong>Mittag-Leffler functions and their applications.</strong> <i>(English)</i> <a class="label nowrap" href="/1218.33021">Zbl 1218.33021</a> </h2> <div class="source"> <a href="/serials/2871" title="Journal Profile">J. Appl. Math.</a> <a href="/?q=in%3A271402" title="Articles in this Issue">2011, Article ID 298628, 51 p. (2011)</a>. </div> <div class="abstract">Summary: Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions, and their interesting and useful properties. Applications of G. M. Mittag-Leffler functions in certain areas of physical and applied sciences are also demonstrated. During the last two decades this function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems of physical, biological, engineering, and earth sciences, and so forth. In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented. An attempt is made to present nearly an exhaustive list of references concerning the Mittag-Leffler functions to make the reader familiar with the present trend of research in Mittag-Leffler type functions and their applications.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A5930812">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A5930812">Cited in <strong>339</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A33E12" title="MSC2020">33E12</a> </td> <td class="space"> Mittag-Leffler functions and generalizations </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1218.33021" data-ciurl="/ci/05930812" data-biburl="/bibtex/05930812.bib" data-amsurl="/amsrefs/05930812.bib" data-xmlurl="/xml/05930812.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05930812.pdf" title="Zbl 1218.33021 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1155/2011/298628" aria-label="DOI for “Mittag-Leffler functions and their applications”" title="10.1155/2011/298628">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/0909.0230"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="mathoverflow"> <h3>Digital Library of Mathematical Functions:</h3> <a href="https://dlmf.nist.gov/10.46#info">§10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions</a><br> <a href="https://dlmf.nist.gov/10.46#p3">§10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions</a><br> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, vol. 3, McGraw-Hill, New York, NY, USA, 1955. · <a href="/0064.06302" class="nowrap">Zbl 0064.06302</a></td> </tr><tr> <td>[2]</td> <td class="space">G. M. Mittag-Leffler, “Une generalisation de l’integrale de Laplace-Abel,” Comptes Rendus de l’Académie des Sciences Série II, vol. 137, pp. 537-539, 1903. · <a href="/34.0434.02" class="nowrap">JFM 34.0434.02</a></td> </tr><tr> <td>[3]</td> <td class="space">G. M. Mittag-Leffler, “Sur la nouvelle fonction E\alpha (x),” Comptes Rendus de l’Académie des Sciences, vol. 137, pp. 554-558, 1903. · <a href="/34.0435.01" class="nowrap">JFM 34.0435.01</a></td> </tr><tr> <td>[4]</td> <td class="space">G. Mittag-Leffler, “Mittag-Leffler, Sur la representation analytiqie d’une fonction monogene (cinquieme note),” Acta Mathematica, vol. 29, no. 1, pp. 101-181, 1905. · <a href="/36.0469.02" class="nowrap">JFM 36.0469.02</a> · <a href="https://doi.org/10.1007/BF02403200" class="nowrap">doi:10.1007/BF02403200</a></td> </tr><tr> <td>[5]</td> <td class="space">A. Wiman, “Über den fundamental satz in der theorie der funcktionen, E\alpha (x),” Acta Mathematica, vol. 29, pp. 191-201, 1905. · <a href="/36.0471.01" class="nowrap">JFM 36.0471.01</a></td> </tr><tr> <td>[6]</td> <td class="space">A. Wiman, “Über die Nullstellun der Funktionen E\alpha (x),” Acta Mathematica, vol. 29, pp. 217-234, 1905. · <a href="/36.0472.01" class="nowrap">JFM 36.0472.01</a></td> </tr><tr> <td>[7]</td> <td class="space">R. P. Agarwai, “A propos d’une note de M. Pierre Humbert,” Comptes Rendus de l’Académie des Sciences, vol. 236, pp. 203-2032, 1953. · <a href="/0051.30801" class="nowrap">Zbl 0051.30801</a></td> </tr><tr> <td>[8]</td> <td class="space">P. Humbert, “Quelques resultants retifs a la fonction de Mittag-Leffler,” Comptes Rendus de l’Académie des Sciences, vol. 236, pp. 1467-1468, 1953. · <a href="/0050.10404" class="nowrap">Zbl 0050.10404</a></td> </tr><tr> <td>[9]</td> <td class="space">P. Humbert and R. P. Agarwal, “Sur la fonction de Mittag-Leffler et quelques unes de ses generalizations,” Bulletin of Science and Mathematics Series II, vol. 77, pp. 180-185, 1953. · <a href="/0052.06402" class="nowrap">Zbl 0052.06402</a></td> </tr><tr> <td>[10]</td> <td class="space">M. M. Dzherbashyan, Integral Transforms and Representations of Functions in the Complex Plane, Nauka, Moscow, Russia, 1966.</td> </tr><tr> <td>[11]</td> <td class="space">K. R. Lang, “Astrophysical Formulae,” in Gas Processes and High-Energy Astrophysics, vol. 1, Springer, New York, NY, USA, 3rd edition, 1999. · <a href="/0957.85002" class="nowrap">Zbl 0957.85002</a></td> </tr><tr> <td>[12]</td> <td class="space">K. R. Lang, “Astrophysical formulae,” in Space, Time, Matter and Cosmology, vol. 2, Springer, New York, NY, USA, 1999. · <a href="/0957.85002" class="nowrap">Zbl 0957.85002</a></td> </tr><tr> <td>[13]</td> <td class="space">R. Hilfer, “Fractional diffusion based on Riemann-Liouville fractional derivatives,” Journal of Physical Chemistry B, vol. 104, no. 3, pp. 914-924, 2000.</td> </tr><tr> <td>[14]</td> <td class="space">R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. · <a href="/0998.26002" class="nowrap">Zbl 0998.26002</a></td> </tr><tr> <td>[15]</td> <td class="space">R. K. Saxena, “Certain properties of generalized Mittag-Leffler function,” in Proceedings of the 3rd Annual Conference of the Society for Special Functions and Their Applications, pp. 77-81, Chennai, India, 2002. · <a href="/1081.33035" class="nowrap">Zbl 1081.33035</a></td> </tr><tr> <td>[16]</td> <td class="space">S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York, NY, USA, 1993. · <a href="/0818.26003" class="nowrap">Zbl 0818.26003</a></td> </tr><tr> <td>[17]</td> <td class="space">E. Hille and J. D. Tamarkin, “On the theory of linear integral equations,” Annals of Mathematics, vol. 31, pp. 479-528, 1930. · <a href="/56.0337.01" class="nowrap">JFM 56.0337.01</a></td> </tr><tr> <td>[18]</td> <td class="space">G. W. S. Blair, “Psychorheology: links between the past and the present,” Journal of Texture Studies, vol. 5, pp. 3-12, 1974.</td> </tr><tr> <td>[19]</td> <td class="space">P. J. Torvik and R. L. Bagley, “On the appearance of the fractional derivative in the behaviour of real materials,” Journal of Applied Mechanics, Transactions ASME, vol. 51, no. 2, pp. 294-298, 1984. · <a href="/1203.74022" class="nowrap">Zbl 1203.74022</a> · <a href="https://doi.org/10.1115/1.3167615" class="nowrap">doi:10.1115/1.3167615</a></td> </tr><tr> <td>[20]</td> <td class="space">M. Caputo and F. Mainardi, “Linear models of dissipation in anelastic solids,” La Rivista del Nuovo Cimento, vol. 1, no. 2, pp. 161-198, 1971. · <a href="https://doi.org/10.1007/BF02820620" class="nowrap">doi:10.1007/BF02820620</a></td> </tr><tr> <td>[21]</td> <td class="space">R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, vol. 1461, Springer, Berlin, Germany, 1991. · <a href="/0717.45002" class="nowrap">Zbl 0717.45002</a> · <a href="https://doi.org/10.1007/BFb0084665" class="nowrap">doi:10.1007/BFb0084665</a></td> </tr><tr> <td>[22]</td> <td class="space">R. Gorenflo and R. Rutman, “On ultraslow and intermediate processes,” in Transform Methods and Special Functions, Sofia, P. Rusev, I. Dimovski, and V. Kiryakova, Eds., pp. 171-183, Science Culture Technology, Singapore, 1995. · <a href="/0923.34005" class="nowrap">Zbl 0923.34005</a></td> </tr><tr> <td>[23]</td> <td class="space">A. A. Kilbas and M. Saigo, “On solutions of integral equations of Abel-Volterra type,” Differential and Integral Equations, vol. 8, pp. 933-1011, 1995. · <a href="/0823.45002" class="nowrap">Zbl 0823.45002</a></td> </tr><tr> <td>[24]</td> <td class="space">R. Gorenflo and Y. Luchko, “Operational methods for solving generalized Abel equations of second kind,” Integral Transforms and Specisl Functiond, vol. 5, pp. 47-58, 1997. · <a href="/0887.44003" class="nowrap">Zbl 0887.44003</a> · <a href="https://doi.org/10.1080/10652469708819125" class="nowrap">doi:10.1080/10652469708819125</a></td> </tr><tr> <td>[25]</td> <td class="space">R. Gorenflo and F. Mainardi, “Fractional oscillations and Mittag-Leffler functions,” Tech. Rep. 1-14/96, Free University of Berlin, Berlin, Germany, 1996. · <a href="/0916.34011" class="nowrap">Zbl 0916.34011</a></td> </tr><tr> <td>[26]</td> <td class="space">R. Gorenflo and F. Mainardi, “Fractional calculus: integral and differential equations of fractional order,” in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 223-276, Springer, Berlin, Germany, 1997.</td> </tr><tr> <td>[27]</td> <td class="space">F. Mainardi and R. Gorenflo, “The Mittag-Leffler function in the Riemann-Liouville fractional calculus,” in Boundary Value Problems, Special Functions and Fractional Calculus, A. A. Kilbas, Ed., pp. 215-225, Byelorussian State University, Minsk, Belarus, 1996.</td> </tr><tr> <td>[28]</td> <td class="space">F. Mainardi and R. Gorenflo, “On Mittag-Leffler-type functions in fractional evolution processes,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 283-299, 2000. · <a href="/0970.45005" class="nowrap">Zbl 0970.45005</a> · <a href="https://doi.org/10.1016/S0377-0427(00)00294-6" class="nowrap">doi:10.1016/S0377-0427(00)00294-6</a></td> </tr><tr> <td>[29]</td> <td class="space">R. Gorenflo, Y. Luchko, and S. V. Rogosin, “Mittag-Leffler type functions, notes on growth properties and distribution of zeros,” Tech. Rep. A04-97, Freie Universität Berlin, Berlin, Germany, 1997.</td> </tr><tr> <td>[30]</td> <td class="space">R. Gorenflo, A. A. Kilbas, and S. V. Rogosin, “On the generalized Mittag-Leffler type function,” Integral Transform Special Functions, vol. 7, no. 3-4, pp. 215-224, 1998. · <a href="/0935.33012" class="nowrap">Zbl 0935.33012</a> · <a href="https://doi.org/10.1080/10652469808819200" class="nowrap">doi:10.1080/10652469808819200</a></td> </tr><tr> <td>[31]</td> <td class="space">Y. U. Luchko, “Operational method in fractional calculus,” Fractional Calculus & Applied Analisys, vol. 2, pp. 463-488, 1999. · <a href="/1030.26009" class="nowrap">Zbl 1030.26009</a></td> </tr><tr> <td>[32]</td> <td class="space">Y. U. F. Luchko and H. M. Srivastava, “The exact solution of certain differential equations of fractional order by using operational calculus,” Computers and Mathematics with Applications, vol. 29, no. 8, pp. 73-85, 1995. · <a href="/0824.44011" class="nowrap">Zbl 0824.44011</a> · <a href="https://doi.org/10.1016/0898-1221(95)00031-S" class="nowrap">doi:10.1016/0898-1221(95)00031-S</a></td> </tr><tr> <td>[33]</td> <td class="space">A. A. Kilbas, M. Saigo, and R. K. Saxena, “Solution of Volterra integro-differential equations with generalized Mittag-Leffler function in the kernels,” Journal of Integral Equations and Applications, vol. 14, no. 4, pp. 377-386, 2002. · <a href="/1041.45011" class="nowrap">Zbl 1041.45011</a> · <a href="https://doi.org/10.1216/jiea/1181074929" class="nowrap">doi:10.1216/jiea/1181074929</a></td> </tr><tr> <td>[34]</td> <td class="space">A. A. Kilbas, M. Saigo, and R. K. Saxena, “Generalized Mittag-Leffler function and generalized fractional calculus operators,” Integral Transforms and Special Functions, vol. 15, no. 1, pp. 31-49, 2004. · <a href="/1047.33011" class="nowrap">Zbl 1047.33011</a> · <a href="https://doi.org/10.1080/10652460310001600717" class="nowrap">doi:10.1080/10652460310001600717</a></td> </tr><tr> <td>[35]</td> <td class="space">R. K. Saxena and M. Saigo, “Certain properties of fractional calculus operators associated with generalized Wright function,” Fractional Calculus & Applied Analisys, vol. 6, pp. 141-154, 2005. · <a href="/1144.26010" class="nowrap">Zbl 1144.26010</a></td> </tr><tr> <td>[36]</td> <td class="space">V. Kiryakova, “Some special functions related to fractional calculus and fractional non-integer order control systems and equations,” Facta Universitatis. Series: Mechanics, Automatic Control and Robotics, vol. 7, no. 1, pp. 79-98, 2008.</td> </tr><tr> <td>[37]</td> <td class="space">V. S. Kiryakova, “Special functions of fractional calculus: recent list, results, applications,” in Proceedings of the 3rd IFC Workshop: Fractional Differentiation and Its Applications (FDA ’08), pp. 1-23, Cankaya University, Ankara, Turkey, November 2008.</td> </tr><tr> <td>[38]</td> <td class="space">R. K. Saxena, S. L. Kalla, and V. S. Kiryakova, “Relations connecting multiindex Mittag-Leffler functions and Riemann-Liouville fractional calculus,” Algebras, Groups and Geometries, vol. 20, pp. 363-385, 2003. · <a href="/1050.33016" class="nowrap">Zbl 1050.33016</a></td> </tr><tr> <td>[39]</td> <td class="space">R. K. Saxena, A. M. Mathai, and H. J. Haubold, “On fractional kinetic equations,” Astrophysics and Space Science, vol. 282, no. 1, pp. 281-287, 2002. · <a href="https://doi.org/10.1023/A:1021175108964" class="nowrap">doi:10.1023/A:1021175108964</a></td> </tr><tr> <td>[40]</td> <td class="space">R. K. Saxena, A. M. Mathai, and H. J. Haubold, “On generalized fractional kinetic equations,” Physica A, vol. 344, no. 3-4, pp. 657-664, 2004. · <a href="https://doi.org/10.1016/j.physa.2004.06.048" class="nowrap">doi:10.1016/j.physa.2004.06.048</a></td> </tr><tr> <td>[41]</td> <td class="space">R. K. Saxena, A. M. Mathai , and H. J. Haubold, “Unified fractional kinetic equations and a fractional diffusion equation,” Astrophysics & Space Science, vol. 290, pp. 241-245, 2004. · <a href="/1115.82300" class="nowrap">Zbl 1115.82300</a></td> </tr><tr> <td>[42]</td> <td class="space">R. K. Saxena, A. M. Mathai, and H. J. Haubold, “Astrophysical thermonuclear functions for Boltzmann-Gibbs statistics and Tsallis statistics,” Physica A, vol. 344, no. 3-4, pp. 649-656, 2004. · <a href="https://doi.org/10.1016/j.physa.2004.06.047" class="nowrap">doi:10.1016/j.physa.2004.06.047</a></td> </tr><tr> <td>[43]</td> <td class="space">R. K. Saxena, A. M. Mathai, and H. J. Haubold, “Fractional reaction-diffusion equations,” Astrophysics and Space Science, vol. 305, no. 3, pp. 289-296, 2006. · <a href="/1105.35307" class="nowrap">Zbl 1105.35307</a> · <a href="https://doi.org/10.1007/s10509-006-9189-6" class="nowrap">doi:10.1007/s10509-006-9189-6</a></td> </tr><tr> <td>[44]</td> <td class="space">R. K. Saxena and S. L. Kalla, “On the solutions of certain fractional kinetic equations,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 504-511, 2008. · <a href="/1166.76051" class="nowrap">Zbl 1166.76051</a> · <a href="https://doi.org/10.1016/j.amc.2007.10.005" class="nowrap">doi:10.1016/j.amc.2007.10.005</a></td> </tr><tr> <td>[45]</td> <td class="space">A. M. Mathai, R. K. Saxena, and H. J. Haubold, “A certain class of Laplace transforms with application in reaction and reaction-diffusion equations,” Astrophysics & Space Science, vol. 305, pp. 283-288, 2006. · <a href="/1105.35301" class="nowrap">Zbl 1105.35301</a> · <a href="https://doi.org/10.1007/s10509-006-9188-7" class="nowrap">doi:10.1007/s10509-006-9188-7</a></td> </tr><tr> <td>[46]</td> <td class="space">H. J. Haubold and A. M. Mathai, “The fractional kinetic equation and thermonuclear functions,” Astrophysics and Space Science, vol. 273, no. 1-4, pp. 53-63, 2000. · <a href="/1034.82048" class="nowrap">Zbl 1034.82048</a> · <a href="https://doi.org/10.1023/A:1002695807970" class="nowrap">doi:10.1023/A:1002695807970</a></td> </tr><tr> <td>[47]</td> <td class="space">H. J. Haubold, A. M. Mathai, and R. K Saxena, “Solution of fractional reaction-diffusion equations in terms of the H-function,” Bulletin of the Astronomical Society of India, vol. 35, pp. 381-689, 2007.</td> </tr><tr> <td>[48]</td> <td class="space">H. M. Srivastava and R. K. Saxena, “Operators of fractional integration and their applications,” Applied Mathematics and Computation, vol. 118, no. 1, pp. 1-52, 2001. · <a href="/1022.26012" class="nowrap">Zbl 1022.26012</a> · <a href="https://doi.org/10.1016/S0096-3003(99)00208-8" class="nowrap">doi:10.1016/S0096-3003(99)00208-8</a></td> </tr><tr> <td>[49]</td> <td class="space">M. N. Berberan-Santos, “Relation between the inverse Laplace transforms of I(t\beta ) and I(t): application to the Mittag-Leffler and asymptotic inverse power law relaxation functions,” Journal of Mathematical Chemistry, vol. 38, no. 2, pp. 265-270, 2005. · <a href="/1217.44003" class="nowrap">Zbl 1217.44003</a> · <a href="https://doi.org/10.1007/s10910-005-5412-x" class="nowrap">doi:10.1007/s10910-005-5412-x</a></td> </tr><tr> <td>[50]</td> <td class="space">H. Pollard, “The completely monotonic character of the Mittag-Leffler function E\alpha ( - x),” Bulletin of the American Mathematical Society, vol. 54, pp. 1115-116, 1948. · <a href="/0033.35902" class="nowrap">Zbl 0033.35902</a> · <a href="https://doi.org/10.1090/S0002-9904-1948-09132-7" class="nowrap">doi:10.1090/S0002-9904-1948-09132-7</a></td> </tr><tr> <td>[51]</td> <td class="space">R. Gorenflo, Y. Luchko, and H. M. Srivastava, “Operational method for solving Gauss’ hypergeometric function as a kernel,” International Journal of Mathematics and Mathematical Sciences, vol. 6, pp. 179-200, 1997. · <a href="/0889.45005" class="nowrap">Zbl 0889.45005</a></td> </tr><tr> <td>[52]</td> <td class="space">R. Gorenflo, J. Loutschko, and Y. Luchko, “Computation of the Mittag-Leffler function and its derivatives,” Fractional Calculus & Applied Analisys, vol. 5, no. 4, pp. 491-518, 2002. · <a href="/1027.33016" class="nowrap">Zbl 1027.33016</a></td> </tr><tr> <td>[53]</td> <td class="space">I. S. Gupta and L. Debnath, “Some properties of the Mittag-Leffler functions,” Integral Transforms and Special Functions, vol. 18, no. 5, pp. 329-336, 2007. · <a href="/1118.33011" class="nowrap">Zbl 1118.33011</a> · <a href="https://doi.org/10.1080/10652460601090216" class="nowrap">doi:10.1080/10652460601090216</a></td> </tr><tr> <td>[54]</td> <td class="space">A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, John Wiley & Sons, New York, NY, USA, 1978. · <a href="/0382.33001" class="nowrap">Zbl 0382.33001</a></td> </tr><tr> <td>[55]</td> <td class="space">A. P. Prudnikov, Y. U. Brychkov, and O. I. Mariche, Integrals and Series, vol. 3 of More Special Functions, Gordon and Breach, New York, NY, USA, 1990. · <a href="/0967.00503" class="nowrap">Zbl 0967.00503</a></td> </tr><tr> <td>[56]</td> <td class="space">A. A. Kilbas and M. Saigo, H-Transforms: Theory and Applications, Analytic Methods and Special Functions, Chapman & Hall, CRC Press, Boca Raton, Fla, USA, 2004. · <a href="/1056.44001" class="nowrap">Zbl 1056.44001</a></td> </tr><tr> <td>[57]</td> <td class="space">E. M. Wright, “The asymptotic expansion of the generalized hypergeometric function,” Journal London Mathematical Society, vol. 10, pp. 286-293, 1935. · <a href="/0013.02104" class="nowrap">Zbl 0013.02104</a> · <a href="https://doi.org/10.1112/jlms/s1-10.40.286" class="nowrap">doi:10.1112/jlms/s1-10.40.286</a></td> </tr><tr> <td>[58]</td> <td class="space">E. M. Wright, “The asymptotic expansion of the integral functions defined by Taylor series,” Philosophical Transactions of the Royal Society A, vol. 238, pp. 423-451, 1940. · <a href="/0023.14002" class="nowrap">Zbl 0023.14002</a> · <a href="https://doi.org/10.1098/rsta.1940.0002" class="nowrap">doi:10.1098/rsta.1940.0002</a></td> </tr><tr> <td>[59]</td> <td class="space">A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, NY, USA, 1953. · <a href="/0052.29502" class="nowrap">Zbl 0052.29502</a></td> </tr><tr> <td>[60]</td> <td class="space">A. A. Kilbas, M. Saigo, and J. J. Trujillo, “On the generalized Wright function,” Fractional Calculus & Applied Analisys, vol. 5, no. 4, pp. 437-460, 2002. · <a href="/1027.33015" class="nowrap">Zbl 1027.33015</a></td> </tr><tr> <td>[61]</td> <td class="space">E. M. Wright, “On the coefficients of power series having exponential singularities,” Journal London Mathematical Society, vol. 8, pp. 71-79, 1933. · <a href="/0006.19704" class="nowrap">Zbl 0006.19704</a> · <a href="https://doi.org/10.1112/jlms/s1-8.1.71" class="nowrap">doi:10.1112/jlms/s1-8.1.71</a></td> </tr><tr> <td>[62]</td> <td class="space">V .S. Kiryakova, Generalized Fractional Calculus and Applications, vol. 301 of Pitman Research Notes in Mathematics, Longman, Harlow, UK; John Wiley & Sons, New York, NY, USA, 1994. · <a href="/0882.26003" class="nowrap">Zbl 0882.26003</a></td> </tr><tr> <td>[63]</td> <td class="space">F. Mainardi, “Fractional calculus: some basic problems in continuum and statistical mechanics,” in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 291-348, Springer, Wien, Germany, 1997. · <a href="/0917.73004" class="nowrap">Zbl 0917.73004</a></td> </tr><tr> <td>[64]</td> <td class="space">E. Buckwar and Y. Luchko, “Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, pp. 81-97, 1998. · <a href="/0932.58038" class="nowrap">Zbl 0932.58038</a> · <a href="https://doi.org/10.1006/jmaa.1998.6078" class="nowrap">doi:10.1006/jmaa.1998.6078</a></td> </tr><tr> <td>[65]</td> <td class="space">Y. U. Luchko and R. Gorenflo, “Scale-invariant solutins of a partial differential equation of fractional order,” Fractional Calculus & Applied Analisys, vol. 1, pp. 63-78, 1998. · <a href="/0940.45001" class="nowrap">Zbl 0940.45001</a></td> </tr><tr> <td>[66]</td> <td class="space">A. A. Kilbas, “Fractional calculus of the generalized Wright function,” Fractional Calculus & Applied Analisys, vol. 8, no. 2, pp. 113-126, 2005. · <a href="/1144.26008" class="nowrap">Zbl 1144.26008</a></td> </tr><tr> <td>[67]</td> <td class="space">T. R. Prabhakar, “A singular integral equation with a generalized Mittag-Leffler function in the kernel,” Yokohama Mathematical Journal, vol. 19, pp. 7-15, 1971. · <a href="/0221.45003" class="nowrap">Zbl 0221.45003</a></td> </tr><tr> <td>[68]</td> <td class="space">E. M. Wright, “The asymptotic expansion of the generalized Bessel function,” Proceedings London Mathematical Society, vol. 38, pp. 257-270, 1934. · <a href="/0010.21103" class="nowrap">Zbl 0010.21103</a> · <a href="https://doi.org/10.1112/plms/s2-38.1.257" class="nowrap">doi:10.1112/plms/s2-38.1.257</a></td> </tr><tr> <td>[69]</td> <td class="space">Y. U. Luchko and S. B. Yaskubovich, “Operational calculus for the generalized fractional differential operator and applications,” Mathematica Balkanica-New Series, vol. 4, no. 2, pp. 119-130, 1990. · <a href="/0830.44004" class="nowrap">Zbl 0830.44004</a></td> </tr><tr> <td>[70]</td> <td class="space">Y. U. Luchko and S. B. Yakubovich, “An operational method for solving some classes of integro-differential equations,” Differentsial’nye Uravneniya, vol. 30, pp. 269-280, 1994 (Russian). · <a href="/0827.44004" class="nowrap">Zbl 0827.44004</a></td> </tr><tr> <td>[71]</td> <td class="space">M. A. Al-Bassam and Y. F. Luchko, “On generalized fractional calculus and its application to the solution of integro-differential equations,” Journal of Fractional Calculus, vol. 7, pp. 69-88, 1995. · <a href="/0840.44002" class="nowrap">Zbl 0840.44002</a></td> </tr><tr> <td>[72]</td> <td class="space">S. B. Hadid and Y. Luchko, “An operational method for solving fractional differential equations of anarbitrary real order,” Pan-American Mathematical Journal, vol. 6, pp. 57-73, 1996. · <a href="/0848.44003" class="nowrap">Zbl 0848.44003</a></td> </tr><tr> <td>[73]</td> <td class="space">R. Gorenflo, A. Iskenderov, and Y. Luchko, “Mapping between solutions of fractional diffusion wave equations,” Fractional Calculus & Applied Analisys, vol. 3, pp. 75-86, 2000. · <a href="/1033.35161" class="nowrap">Zbl 1033.35161</a></td> </tr><tr> <td>[74]</td> <td class="space">R. Gorenflo, Y. Luchko, and F. Mainardi, “Wright functions as scale-invariant solutions of the diffusion-wave equation,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 175-191, 2000. · <a href="/0973.35012" class="nowrap">Zbl 0973.35012</a> · <a href="https://doi.org/10.1016/S0377-0427(00)00288-0" class="nowrap">doi:10.1016/S0377-0427(00)00288-0</a></td> </tr><tr> <td>[75]</td> <td class="space">Y. U. Luchko and R. Gorenflo, “An operational method for solving fractional differential equations with a Caputo derivative,” Acta Mathematica Vietnamica, vol. 24, pp. 207-234, 1999. · <a href="/0931.44003" class="nowrap">Zbl 0931.44003</a></td> </tr><tr> <td>[76]</td> <td class="space">A. A. Kilbas and M. Saigo, “Fractional integrals and derivatives of Mittag-Leffler type function,” Doklady Akademii Nauk Belarusi, vol. 39, no. 4, pp. 22-26, 1995 (Russian).</td> </tr><tr> <td>[77]</td> <td class="space">A. A. Kilbas and M. Saigo, “On mittag-leffler type function, fractional calculus operators and solutions of integral equations,” Integral Transforms and Special Functions, vol. 4, no. 4, pp. 355-370, 1996. · <a href="/0876.26007" class="nowrap">Zbl 0876.26007</a> · <a href="https://doi.org/10.1080/10652469608819121" class="nowrap">doi:10.1080/10652469608819121</a></td> </tr><tr> <td>[78]</td> <td class="space">K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. · <a href="/0789.26002" class="nowrap">Zbl 0789.26002</a></td> </tr><tr> <td>[79]</td> <td class="space">A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, vol. 2, McGraw-Hill, New York, NY, USA, 1954. · <a href="/0055.36401" class="nowrap">Zbl 0055.36401</a></td> </tr><tr> <td>[80]</td> <td class="space">K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974. · <a href="/0292.26011" class="nowrap">Zbl 0292.26011</a></td> </tr><tr> <td>[81]</td> <td class="space">M. Caputo, Elasticitá e Dissipazione, Zanichelli, Bologna, Italy, 1969.</td> </tr><tr> <td>[82]</td> <td class="space">I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999. · <a href="/0924.34008" class="nowrap">Zbl 0924.34008</a></td> </tr><tr> <td>[83]</td> <td class="space">R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: a fractional dynamics approach,” Physics Report, vol. 339, no. 1, pp. 1-77, 2000. · <a href="/0984.82032" class="nowrap">Zbl 0984.82032</a> · <a href="https://doi.org/10.1016/S0370-1573(00)00070-3" class="nowrap">doi:10.1016/S0370-1573(00)00070-3</a></td> </tr><tr> <td>[84]</td> <td class="space">A. Compte, “Stochastic foundations of fractional dynamics,” Physical Review E, vol. 53, no. 4, pp. 4191-4193, 1996.</td> </tr><tr> <td>[85]</td> <td class="space">B. N. Al-Saqabi and VU. K. Tuan, “Solution of a fractional differintegral equation,” Integral Transforms and Special Functions, vol. 4, no. 4, pp. 321-326, 1996. · <a href="/0864.34002" class="nowrap">Zbl 0864.34002</a> · <a href="https://doi.org/10.1080/10652469608819118" class="nowrap">doi:10.1080/10652469608819118</a></td> </tr><tr> <td>[86]</td> <td class="space">V. S. Kiryakova, “Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 241-259, 2000. · <a href="/0966.33011" class="nowrap">Zbl 0966.33011</a> · <a href="https://doi.org/10.1016/S0377-0427(00)00292-2" class="nowrap">doi:10.1016/S0377-0427(00)00292-2</a></td> </tr><tr> <td>[87]</td> <td class="space">M. M. Dzherbashyan, “On the integral transformations generated by the generalzied Mittag-Leffler fuction,” Izdatel’stvo Akademii Nauk Armyanskoi SSR, vol. 13, no. 3, pp. 21-63, 1960 (Russian).</td> </tr><tr> <td>[88]</td> <td class="space">V. S. Kiryakova, “Multiindex Mittag-Leffler functions related to Gelfond-Leontiev operators and Laplace type integral transforms,” Fractional Calculus & Applied Analisys, vol. 2, pp. 4445-462, 1999. · <a href="/1111.33300" class="nowrap">Zbl 1111.33300</a></td> </tr><tr> <td>[89]</td> <td class="space">S. Sharma, “Fractional differentiation and fractional integration of the M-series,” Fractional Calculus & Applied Analisys, vol. 11, pp. 187-191, 2008. · <a href="/1153.26303" class="nowrap">Zbl 1153.26303</a></td> </tr><tr> <td>[90]</td> <td class="space">R. K. Saxena, “A remark on a paper on M-series,” Fractional Calculus & Applied Analisys, vol. 12, no. 1, pp. 109-110, 2009. · <a href="/1177.26013" class="nowrap">Zbl 1177.26013</a></td> </tr><tr> <td>[91]</td> <td class="space">R. N. Pillai, “On Mittag-Leffler functions and related distributions,” Annals of the Institute of Statistical Mathematics, vol. 42, no. 1, pp. 157-161, 1990. · <a href="/0714.60009" class="nowrap">Zbl 0714.60009</a> · <a href="https://doi.org/10.1007/BF00050786" class="nowrap">doi:10.1007/BF00050786</a></td> </tr><tr> <td>[92]</td> <td class="space">A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists, Springer, New York, NY, USA, 2008. · <a href="/1151.33001" class="nowrap">Zbl 1151.33001</a></td> </tr><tr> <td>[93]</td> <td class="space">K. Jayakumar, “Mittag-Leffler process,” Mathematical and Computer Modelling, vol. 37, no. 12-13, pp. 1427-1434, 2003. · <a href="/1045.62087" class="nowrap">Zbl 1045.62087</a> · <a href="https://doi.org/10.1016/S0895-7177(03)90050-1" class="nowrap">doi:10.1016/S0895-7177(03)90050-1</a></td> </tr><tr> <td>[94]</td> <td class="space">K. Jayakumar and R. P. Suresh, “Mittag-Leffler distribution,” Journal of the Indian Society of Probability and Statistics, vol. 7, pp. 51-71, 2003.</td> </tr><tr> <td>[95]</td> <td class="space">A. M. Mathai, A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford, UK, 1993. · <a href="/0770.33001" class="nowrap">Zbl 0770.33001</a></td> </tr><tr> <td>[96]</td> <td class="space">G. D. Lin, “On the Mittag-Leffler distribution,” Journal of Statistical Planning and Inference, vol. 74, pp. 1-9, 1998. · <a href="/0935.60002" class="nowrap">Zbl 0935.60002</a></td> </tr><tr> <td>[97]</td> <td class="space">A. M. Mathai, “A pathway to matrix-variate gamma and normal densities,” Linear Algebra and Its Applications, vol. 396, no. 1-3, pp. 317-328, 2005. · <a href="/1084.62044" class="nowrap">Zbl 1084.62044</a> · <a href="https://doi.org/10.1016/j.laa.2004.09.022" class="nowrap">doi:10.1016/j.laa.2004.09.022</a></td> </tr><tr> <td>[98]</td> <td class="space">R. N. Pillai and K. Jayakumar, “Discrete Mittag-Leffler distributions,” Statistics and Probability Letters, vol. 23, no. 3, pp. 271-274, 1995. · <a href="/0829.60010" class="nowrap">Zbl 0829.60010</a> · <a href="https://doi.org/10.1016/0167-7152(94)00124-Q" class="nowrap">doi:10.1016/0167-7152(94)00124-Q</a></td> </tr><tr> <td>[99]</td> <td class="space">A. G. Pakes, “Mixture representations for symmetric generalized Linnik laws,” Statistics and Probability Letters, vol. 37, no. 3, pp. 213-221, 1998. · <a href="/1246.60024" class="nowrap">Zbl 1246.60024</a></td> </tr><tr> <td>[100]</td> <td class="space">F. Mainardi and G. Pagnini, “Mellin-Barnes integrals for stable distributions and their convolutions,” Fractional Calculus & Applied Analysis, vol. 11, no. 4, pp. 443-456, 2008. · <a href="/1175.26017" class="nowrap">Zbl 1175.26017</a></td> </tr><tr> <td>[101]</td> <td class="space">S. C. Lim and L. P. Teo, “Analytic and asymptotic properties of multivariate generalized Linnik’s probability densities,” Journal of Fourier Analysis and Applications, pp. 1-33, 2009. · <a href="/1202.60028" class="nowrap">Zbl 1202.60028</a> · <a href="https://doi.org/10.1007/s00041-009-9097-6" class="nowrap">doi:10.1007/s00041-009-9097-6</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1218.33021 - zbMATH Open