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Formula Search - zbMATH Open
<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Formula Search - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive"> <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" class="start"> <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="/formulae/?q=m+%3C+%5Cinfty"> <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" 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<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" class="start"> <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"> <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 active"> <a href="/formulae/">Formul忙</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div id="formulae"> <div class="content-formular"> <form class="form-inline" name="formulae" method="GET" action="/"> <div class="formulae one-line" style="display: block;"> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input id="MathInput" onkeyup="Preview.Update()" class="query form-control" type="text" name="f" value="m < \infty" aria-label="Search for mathematical formulae" placeholder="Search for mathematical formul忙" 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 examples" style="z-index:2"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown">Examples <i class="caret"></i></button> <ul class="dropdown-menu pull-right"> <li><a tabindex="0"><span class="text">limit</span><span class="formula">\lim_{?a\rightarrow 0} ?x</span>Limit</a></li> <li><a tabindex="0"><span class="text">Fermat</span><span class="formula">?a^?n + ?b^?n=?c^?n</span>Fermat's Theorem</a></li> <li><a tabindex="0"><span class="text">polynomial</span><span class="formula">P(?x)</span>Polynomial</a></li> <li><a tabindex="0"><span class="text">probability</span><span class="formula">P(?x)</span>Probability</a></li> <li><a tabindex="0"><span class="text">chain</span><span class="formula">0 \leq ?i \leq ?n</span>Inequality chain</a></li> <li><a tabindex="0"><span class="text">periodic</span><span class="formula">?f(?x + ?k) = ?f(?x)</span>Periodic function</a></li> <li><a tabindex="0"><span class="text">logistic</span><span class="formula">\lambda ?x (1 - ?x)</span>Logistic map</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 target="mathweb" href="/formulae/?q=m+%3C+%5Cinfty">m < \infty </a></span> <span class="search-explanation" role="cell">Queries are formulated in <sdiv class="help-item"ong>LaTeX</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a target="mathweb" href="/formulae/?q=%5Csin%28x%29">\sin(x)</a></span> <span class="search-explanation" role="cell">Standard <sdiv class="help-item"ong>math commands</strong> are supported but mathematical variables are not instantiated.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a target="mathweb" href="/formulae/?q=%3Fa%5E2+%2B+%3Fb%5E2">?a^2 + ?b^2</a></span> <span class="search-explanation" role="cell"><sdiv class="help-item"ong>Search variables</strong> should be marked by a preceding <strong>question mark</strong> and ended by <strong>whitespace characters</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a target="mathweb" href="/formulae/?q=%3Fa%2B%3Fb+%3D+%3Fb%2B%3Fa">?a+?b = ?b+?a</a></span> <span class="search-explanation" role="cell">Variables can occur multiple times and receive <strong>identical instantiations</strong>; this query matches commutativity.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a target="mathweb" href="/formulae/?q=%3Ff%28%3Fa%2B%3Fb%29">?f(?a+?b)</a></span> <span class="search-explanation" role="cell">Query variables are also allowed in <strong>functional position</strong>.</span> </div> </div></div> </div> </form> <div class="clear"></div> <div class="preview" style="min-height:80px"> <div id="MathPreview"></div> <div id="MathBuffer" style="visibility:hidden; position:absolute;"></div> </div> <div class="clearfix"></div> <div id="start" class="start"> <p class="banner"> The formula search is now integrated into the <a href="/?show_structured=1">structured zbMATH Open search</a>, which allows for free combination with other query types. Furthermore, formula queries (as, e.g., given in the <a href="/?show_structured=1&show_examples=1">Examples</a>) can be refined via the filter functions. </p> <p class="banner"> The zbMATH Open formula search uses the <a href="https://github.com/MathWebSearch/mws">MathWebSearch system</a>, which is a content-based search engine for MathML formulae based on substitution tree indexing. The first prototype is a result of a joint research project of <a href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe</a> with the <a href="http://www.jacobs-university.de/">Jacobs University Bremen</a>, funded by the <a href="http://www.leibniz-gemeinschaft.de/en/home/">Leibniz Association</a>, which aims at developing concepts and methods for a semantic analysis and retrieval of mathematical formulae in the zbMATH Open corpus. </p> </div> </div> </div> </div> <div id="body"> <div id="main" class="start"> <div class="messages"> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="logos"> <a class="logo no-new-tab-icon" href="https://www.fiz-karlsruhe.de/en" target="fiz"> <img class="fiz" src="/static/fiz.gif" alt="logo of FIZ Karlsruhe GmbH" title="FIZ Karlsruhe (opens in new tab)"> </a> <a class="logo no-new-tab-icon" href="https://euromathsoc.org/" target="ems"> <img class="ems" src="/static/ems.gif" alt="logo of The European Mathematical Society" title="The European Mathematical Society (opens in new tab)"> </a> <a class="logo no-new-tab-icon" href="https://www.hadw-bw.de/" target="haw"> <img class="haw" src="/static/haw.gif" alt="logo of Heidelberg Academy of Sciences and Humanities" title="Heidelberg Academy of Sciences and Humanities (opens in new tab)"> </a> </div> <div class="clearfix"></div><div class="copyright"> © 2024 <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/javascript"> var Preview = { delay: 100, preview: null, buffer: null, timeout: null, mjRunning: false, oldText: null, Init: function () { this.preview = document.getElementById("MathPreview"); this.buffer = document.getElementById("MathBuffer"); }, SwapBuffers: function () { var buffer = this.preview, preview = this.buffer; this.buffer = buffer; this.preview = preview; buffer.style.visibility = "hidden"; buffer.style.position = "absolute"; preview.style.position = ""; preview.style.visibility = ""; }, Update: function () { if (this.timeout) {clearTimeout(this.timeout)} this.timeout = setTimeout(this.callback,this.delay); }, CreatePreview: function () { Preview.timeout = null; if (this.mjRunning) return; var text = document.getElementById("MathInput").value; text = text.replace(/\?([a-z0-9])/gi, '\{\\color{red}$1}') if (text) { text = "\\(" + text + "\\)"; } if (text === this.oldtext) return; this.buffer.innerHTML = this.oldtext = text; this.mjRunning = true; MathJax.Hub.Queue( [ "Typeset", MathJax.Hub, this.buffer ], [ "PreviewDone", this ] ); }, PreviewDone: function () { this.mjRunning = false; this.SwapBuffers(); $(window).resize(); } }; Preview.callback = MathJax.Callback(["CreatePreview",Preview]); Preview.callback.autoReset = true; Preview.Init(); </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>