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<!DOCTYPE html><html lang="en"> <head> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <title>DLMF: About the Project</title> <link rel="shortcut icon" href=".././style/DLMF-16.png" type="image/png"> <script type="text/javascript"></script> <script type="text/javascript" src=".././style/jquery.js"></script> <script type="text/javascript" src=".././style/jquery.leaveNotice.js"></script> <script type="text/javascript" src=".././style/DLMF.js"></script> <script async="" type="text/javascript" id="_fed_an_ua_tag" src="https://dap.digitalgov.gov/Universal-Federated-Analytics-Min.js?agency=DOC&subagency=NIST&pua=UA-37115410-44&yt=true&exts=ppsx,pps,f90,sch,rtf,wrl,txz,m1v,xlsm,msi,xsd,f,tif,eps,mpg,xml,pl,xlt,c"></script><script async="" src="https://www.googletagmanager.com/gtag/js?id=G-BZB64W4M0L"></script><script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-BZB64W4M0L'); </script> <link rel="stylesheet" type="text/css" href=".././style/LaTeXML.css"> <link rel="stylesheet" type="text/css" href=".././style/DLMF.css"> <link rel="stylesheet" type="text/css" href=".././style/print.css" media="print"> <meta name="viewport" content="width=device-width, initial-scale=1"> <link rel="top" href=".././" title="DLMF"> <link rel="copyright" href=".././about/notices" title="Copyright"> <link rel="search" href=".././search/search" title="Search"> <link rel="help" class="ltx_help" href=".././help/" title="Help"> <link rel="start" href=".././" title=""> <link rel="prev" href=".././search/" title="Advanced Search"> <link rel="next" href=".././about/notices" title="Notices ‣ About the Project"> <link rel="document" href=".././front/foreword" title="Foreword"> <link rel="document" href=".././front/preface" title="Preface"> <link rel="document" href=".././front/introduction" title="Mathematical Introduction"> <link rel="chapter" href=".././1" title="Chapter 1 Algebraic and Analytic Methods"> <link rel="chapter" href=".././2" title="Chapter 2 Asymptotic Approximations"> <link rel="chapter" href=".././3" title="Chapter 3 Numerical Methods"> <link rel="chapter" href=".././4" title="Chapter 4 Elementary Functions"> <link rel="chapter" href=".././5" title="Chapter 5 Gamma Function"> <link rel="chapter" href=".././6" title="Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals"> <link rel="chapter" href=".././7" title="Chapter 7 Error Functions, Dawson’s and Fresnel Integrals"> <link rel="chapter" href=".././8" title="Chapter 8 Incomplete Gamma and Related Functions"> <link rel="chapter" href=".././9" title="Chapter 9 Airy and Related Functions"> <link rel="chapter" href=".././10" title="Chapter 10 Bessel Functions"> <link rel="chapter" href=".././11" title="Chapter 11 Struve and Related Functions"> <link rel="chapter" href=".././12" title="Chapter 12 Parabolic Cylinder Functions"> <link rel="chapter" href=".././13" title="Chapter 13 Confluent Hypergeometric Functions"> <link rel="chapter" href=".././14" title="Chapter 14 Legendre and Related Functions"> <link rel="chapter" href=".././15" title="Chapter 15 Hypergeometric Function"> <link rel="chapter" href=".././16" title="Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function"> <link rel="chapter" href=".././17" title="Chapter 17 𝑞-Hypergeometric and Related Functions"> <link rel="chapter" href=".././18" title="Chapter 18 Orthogonal Polynomials"> <link rel="chapter" href=".././19" title="Chapter 19 Elliptic Integrals"> <link rel="chapter" href=".././20" title="Chapter 20 Theta Functions"> <link rel="chapter" href=".././21" title="Chapter 21 Multidimensional Theta Functions"> <link rel="chapter" href=".././22" title="Chapter 22 Jacobian Elliptic Functions"> <link rel="chapter" href=".././23" title="Chapter 23 Weierstrass Elliptic and Modular Functions"> <link rel="chapter" href=".././24" title="Chapter 24 Bernoulli and Euler Polynomials"> <link rel="chapter" href=".././25" title="Chapter 25 Zeta and Related Functions"> <link rel="chapter" href=".././26" title="Chapter 26 Combinatorial Analysis"> <link rel="chapter" href=".././27" title="Chapter 27 Functions of Number Theory"> <link rel="chapter" href=".././28" title="Chapter 28 Mathieu Functions and Hill’s Equation"> <link rel="chapter" href=".././29" title="Chapter 29 Lamé Functions"> <link rel="chapter" href=".././30" title="Chapter 30 Spheroidal Wave Functions"> <link rel="chapter" href=".././31" title="Chapter 31 Heun Functions"> <link rel="chapter" href=".././32" title="Chapter 32 Painlevé Transcendents"> <link rel="chapter" href=".././33" title="Chapter 33 Coulomb Functions"> <link rel="chapter" href=".././34" title="Chapter 34 3⁢𝑗,6⁢𝑗,9⁢𝑗 Symbols"> <link rel="chapter" href=".././35" title="Chapter 35 Functions of Matrix Argument"> <link rel="chapter" href=".././36" title="Chapter 36 Integrals with Coalescing Saddles"> <link rel="bibliography" href=".././bib/" title="Bibliography"> <link rel="index" href=".././idx/" title="Index"> <link rel="glossary" href=".././not/" title="Notations"> <link rel="document" href=".././lof/" title="List of Figures"> <link rel="document" href=".././lot/" title="List of Tables"> <link rel="document" href=".././software/" title="Software Index"> <link rel="document" href=".././errata/" title="Errata"> <link rel="document" href=".././help/" title="Need Help?"> <link rel="document" href=".././search/" title="Advanced Search"> <link rel="document" href=".././about/notices" title="Notices ‣ About the Project"> <link rel="document" href=".././about/preface" title="Preface ‣ About the Project"> <link rel="document" href=".././about/sponsors" title="Funding ‣ About the Project"> <link rel="document" href=".././about/news/" title="DLMF Project News ‣ About the Project"> <link rel="document" href=".././about/publications/" title="DLMF Related Publications ‣ About the Project"> <link rel="document" href=".././about/staff" title="Project Staff ‣ About the Project"> <link rel="document" href=".././about/bio/MJAblowitz" title="Profile Mark J. Ablowitz ‣ About the Project"> <link rel="document" href=".././about/bio/GEAndrews" title="Profile George E. Andrews ‣ About the Project"> <link rel="document" href=".././about/bio/BAntonishek" title="Profile Brian Antonishek ‣ About the Project"> <link rel="document" href=".././about/bio/TMApostol" title="Profile Tom M. Apostol ‣ About the Project"> <link rel="document" href=".././about/bio/RAAskey" title="Profile Richard A. Askey ‣ About the Project"> <link rel="document" href=".././about/bio/ARBarnett" title="Profile Antony Ross Barnett ‣ About the Project"> <link rel="document" href=".././about/bio/MVBerry" title="Profile Michael V. Berry ‣ About the Project"> <link rel="document" href=".././about/bio/AIBobenko" title="Profile Alexander I. Bobenko ‣ About the Project"> <link rel="document" href=".././about/bio/RFBoisvert" title="Profile Ronald F. Boisvert ‣ About the Project"> <link rel="document" href=".././about/bio/BLJBraaksma" title="Profile Boele L. J. Braaksma ‣ About the Project"> <link rel="document" href=".././about/bio/DMBressoud" title="Profile David M. Bressoud ‣ About the Project"> <link rel="document" href=".././about/bio/BCCarlson" title="Profile Bille C. Carlson ‣ About the Project"> <link rel="document" href=".././about/bio/CWClark" title="Profile Charles W. Clark ‣ About the Project"> <link rel="document" href=".././about/bio/PAClarkson" title="Profile Peter A. Clarkson ‣ About the Project"> <link rel="document" href=".././about/bio/HCohl" title="Profile Howard S. Cohl ‣ About the Project"> <link rel="document" href=".././about/bio/JEConlon" title="Profile Joyce E. Conlon ‣ About the Project"> <link rel="document" href=".././about/bio/AAMCuyt" title="Profile Annie A. M. Cuyt ‣ About the Project"> <link rel="document" href=".././about/bio/ABOldeDaalhuis" title="Profile Adri B. Olde Daalhuis ‣ About the Project"> <link rel="document" href=".././about/bio/PJDavis" title="Profile Philip J. Davis ‣ About the Project"> <link rel="document" href=".././about/bio/BDeconinck" title="Profile Bernard Deconinck ‣ About the Project"> <link rel="document" href=".././about/bio/KDilcher" title="Profile Karl Dilcher ‣ About the Project"> <link rel="document" href=".././about/bio/DDominici" title="Profile Diego Dominici ‣ About the Project"> <link rel="document" href=".././about/bio/TMDunster" title="Profile T. Mark Dunster ‣ About the Project"> <link rel="document" href=".././about/bio/FGarvan" title="Profile Frank Garvan ‣ About the Project"> <link rel="document" href=".././about/bio/IGessel" title="Profile Ira Gessel ‣ About the Project"> <link rel="document" href=".././about/bio/AGil" title="Profile Amparo Gil ‣ About the Project"> <link rel="document" href=".././about/bio/CJHowls" title="Profile Christopher J. Howls ‣ About the Project"> <link rel="document" href=".././about/bio/MEHIsmail" title="Profile Mourad E.H. Ismail ‣ About the Project"> <link rel="document" href=".././about/bio/AIts" title="Profile Alexander A. Its ‣ About the Project"> <link rel="document" href=".././about/bio/BRJudd" title="Profile Brian R. Judd ‣ About the Project"> <link rel="document" href=".././about/bio/RKoekoek" title="Profile Roelof Koekoek ‣ About the Project"> <link rel="document" href=".././about/bio/THKoornwinder" title="Profile Tom H. Koornwinder ‣ About the Project"> <link rel="document" href=".././about/bio/VBKuznetsov" title="Profile Vadim B. Kuznetsov ‣ About the Project"> <link rel="document" href=".././about/bio/DWLozier" title="Profile Daniel W. Lozier ‣ About the Project"> <link rel="document" href=".././about/bio/LCMaximon" title="Profile Leonard C. Maximon ‣ About the Project"> <link rel="document" href=".././about/bio/MAMcClain" title="Profile Marjorie A. McClain ‣ About the Project"> <link rel="document" href=".././about/bio/BRMiller" title="Profile Bruce R. Miller ‣ About the Project"> <link rel="document" href=".././about/bio/VHMoll" title="Profile Victor Moll ‣ About the Project"> <link rel="document" href=".././about/bio/RJMuirhead" title="Profile Robb J. Muirhead ‣ About the Project"> <link rel="document" href=".././about/bio/GNemes" title="Profile Gergő Nemes ‣ About the Project"> <link rel="document" href=".././about/bio/ENeuman" title="Profile Edward Neuman ‣ About the Project"> <link rel="document" href=".././about/bio/MNewman" title="Profile Morris Newman ‣ About the Project"> <link rel="document" href=".././about/bio/IOlkin" title="Profile Ingram Olkin ‣ About the Project"> <link rel="document" href=".././about/bio/FWJOlver" title="Profile Frank W. J. Olver ‣ About the Project"> <link rel="document" href=".././about/bio/RBParis" title="Profile Richard B. Paris ‣ About the Project"> <link rel="document" href=".././about/bio/PPaule" title="Profile Peter Paule ‣ About the Project"> <link rel="document" href=".././about/bio/JWPitman" title="Profile Jim Pitman ‣ About the Project"> <link rel="document" href=".././about/bio/WPReinhardt" title="Profile William P. Reinhardt ‣ About the Project"> <link rel="document" href=".././about/bio/DSPRichards" title="Profile Donald St. P. Richards ‣ About the Project"> <link rel="document" href=".././about/bio/RRoy" title="Profile Ranjan Roy ‣ About the Project"> <link rel="document" href=".././about/bio/SRuijsenaars" title="Profile Simon Ruijsenaars ‣ About the Project"> <link rel="document" href=".././about/bio/BVSaunders" title="Profile Bonita V. Saunders ‣ About the Project"> <link rel="document" href=".././about/bio/BISchneider" title="Profile Barry I. Schneider ‣ About the Project"> <link rel="document" href=".././about/bio/JJSegura" title="Profile Javier Segura ‣ About the Project"> <link rel="document" href=".././about/bio/BDSleeman" title="Profile Brian D. Sleeman ‣ About the Project"> <link rel="document" href=".././about/bio/RFSwarttouw" title="Profile René F. Swarttouw ‣ About the Project"> <link rel="document" href=".././about/bio/NMTemme" title="Profile Nico M. Temme ‣ About the Project"> <link rel="document" href=".././about/bio/IJThompson" title="Profile Ian J. Thompson ‣ About the Project"> <link rel="document" href=".././about/bio/HVolkmer" title="Profile Hans Volkmer ‣ About the Project"> <link rel="document" href=".././about/bio/PLWalker" title="Profile Peter L. Walker ‣ About the Project"> <link rel="document" href=".././about/bio/GWiersma" title="Profile Gloria Wiersma ‣ About the Project"> <link rel="document" href=".././about/bio/SMWatt" title="Profile Stephen M. Watt ‣ About the Project"> <link rel="document" href=".././about/bio/QWang" title="Profile Qiming Wang ‣ About the Project"> <link rel="document" href=".././about/bio/GWolf" title="Profile Gerhard Wolf ‣ About the Project"> <link rel="document" href=".././about/bio/RWong" title="Profile Roderick S. C. Wong ‣ About the Project"> <link rel="document" href=".././about/bio/AYoussef" title="Profile Abdou Youssef ‣ About the Project"> <link rel="document" href=".././about/bio/JVanderJeugt" title="Profile Joris Van der Jeugt ‣ About the Project"> <link rel="document" href=".././about/bio/WGroenevelt" title="Profile Wolter Groenevelt ‣ About the Project"> <link rel="document" href=".././about/bio/WZudilin" title="Profile Wadim Zudilin ‣ About the Project"> </head> <body class="color_default textfont_default titlefont_default fontsize_default navbar_default"> <div class="ltx_page_navbar"> <div class="ltx_page_navlogo"><a href=".././" title="Digital Library of Mathematical Functions"><span>DLMF</span></a></div> <div class="ltx_page_navitems"> <form method="get" action=".././search/search"> <ul> <li><a href=".././idx/">Index</a></li> <li><a href=".././not/">Notations</a></li> <li><small><input type="text" name="q" value="" size="6" class="ltx_page_navitem_search"><button type="submit">Search</button></small></li> <li><a href=".././help/" class="ltx_help">Help?</a></li> <li><a href=".././help/cite">Citing</a></li> <li><a href=".././help/customize" class="ltx_customize">Customize</a></li> </ul> </form> </div> <div class="ltx_page_navsponsors"> <div><a href=".././about/" class="ltx_page_navabout">About the Project</a></div> </div> </div> <div class="ltx_page_main"> <div class="ltx_page_header"> <a href=".././search/" title="" class="ltx_ref" rel="prev"><span class="ltx_text ltx_ref_title">Advanced Search</span></a><a href=".././about/notices" title="In About the Project" class="ltx_ref" rel="next"><span class="ltx_text ltx_ref_title">Notices</span></a> </div> <div class="ltx_page_content"> <article class="ltx_document ltx_leqno"> <h1 class="ltx_title ltx_title_document">About the Project</h1> <div id="p1" class="ltx_para"> <p class="ltx_p ltx_align_center"><math class="ltx_Math" altimg="m1.png" altimg-height="21px" altimg-valign="-4px" altimg-width="18px" alttext="\Diamond" display="inline"><mi mathvariant="normal">◇</mi></math> <a href=".././about/staff" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Staff</span></a> <math class="ltx_Math" altimg="m1.png" altimg-height="21px" altimg-valign="-4px" altimg-width="18px" alttext="\Diamond" display="inline"><mi mathvariant="normal">◇</mi></math> <a href=".././about/sponsors" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Funding</span></a> <math class="ltx_Math" altimg="m1.png" altimg-height="21px" altimg-valign="-4px" altimg-width="18px" alttext="\Diamond" display="inline"><mi mathvariant="normal">◇</mi></math> <a href=".././about/publications/" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Publications</span></a> <math class="ltx_Math" altimg="m1.png" altimg-height="21px" altimg-valign="-4px" altimg-width="18px" alttext="\Diamond" display="inline"><mi mathvariant="normal">◇</mi></math></p> </div> <figure id="F1" class="ltx_figure"><img src=".././about/g1.jpg" class="ltx_graphics ltx_centering ltx_img_landscape" width="692" height="522" alt="Refer to caption"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 1: </span> The Editors and 9 of the 10 Associate Editors of the DLMF Project (photo taken at 3rd Editors Meeting, April, 2001). The front row, from left to right: Ronald F. Boisvert, Charles W. Clark, Frank W. J. Olver, Daniel W. Lozier, and Michael V. Berry. The back row, from left to right: William P. Reinhardt, Nico M. Temme, Peter Paule, Richard A. Askey, Ingram Olkin, Leonard C. Maximon, Morris Newman, and Walter Gautschi. The tenth Associate Editor, Jet Wimp, is not shown. </figcaption> </figure> <div id="p2" class="ltx_para"> <p class="ltx_p">The Digital Library of Mathematical Functions (DLMF) Project was initiated to perform a complete revision of Abramowitz and Stegun’s <cite class="ltx_cite"><a href=".././bib/#bib24" title="Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" class="ltx_ref">Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables</a></cite>, published in 1964 by the National Bureau of Standards. See <cite class="ltx_cite ltx_citemacro_citet">R. F. Boisvert and D. W. Lozier (<a href=".././about/publications/#bib.bib7" title="" class="ltx_ref">2001</a>)</cite> for historical background about this important publication. The DLMF Project has updated and expanded the coverage for current needs. The results have been published in book form as the <a href="http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521192255" title="" class="ltx_ref ltx_href external">NIST Handbook of Mathematical Functions</a>, by <a href="http://www.cambridge.org/" title="" class="ltx_ref ltx_href external">Cambridge University Press</a>, and disseminated in the free electronic <a href="http://dlmf.nist.gov" title="" class="ltx_ref ltx_href">Digital Library of Mathematical Functions</a>. These products resulted from the leadership of the Editors and Associate Editors pictured in Figure <a href="#F1" title="Figure 1 ‣ About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_tag">1</span></a>; the contributions of 29 authors, 10 validators, and 5 principal developers; and assistance from a large group of contributing developers, consultants, assistants and interns. Details of the early history of the DLMF Project are given in the <a href=".././front/preface" title="" class="ltx_ref"><span class="ltx_text ltx_ref_title">Preface</span></a> and on pp. ix–xi in the <a href="http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521192255" title="" class="ltx_ref ltx_href external">NIST Handbook of Mathematical Functions</a>. See also the list of <a href=".././about/publications/" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Publications</span></a> for further background information.</p> </div> <div id="p3" class="ltx_para"> <p class="ltx_p">After the death in April 2013 of Frank W. J. Olver, Editor-in-Chief and Mathematics Editor of the DLMF, the other Editors initiated an effort aimed at updating the organizational structure of the DLMF project. Since that time there have been a number of developments. Whereas before the project had Editors and Associate Editors, it now has Editors, Senior Associate Editors, and Associate Editors.</p> </div> <div id="p4" class="ltx_para"> <p class="ltx_p">The current Editors are listed on the <a href=".././about/staff" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Staff</span></a> page. It was fortunate that the project had already recruited Adri Olde Daalhuis from the University of Edinburgh in 2012 to serve as an additional Mathematics Editor. Subsequently, the list of Editors has been expanded to include Bruce R. Miller as Information Technology Editor, Bonita V. Saunders as Visualization Editor, Barry I. Schneider as General Editor, Howard S. Cohl as Technical Editor, and Marje A. McClain as Associate Technical Editor. As before, the Editors have primary responsibility for the executive management of the project.</p> </div> <div id="p5" class="ltx_para"> <p class="ltx_p">The former title of Associate Editor has been changed to Senior Associate Editor. Ten Senior Assocate Editors have been named. They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web. Their responsibility is to advise the Editors on future directions for the DLMF.</p> </div> <div id="p6" class="ltx_para"> <p class="ltx_p">The new category of Associate Editor has been created to provide expert advice and assistance for the individual chapters of the DLMF. Twenty-six Associate Editors have been named. They will be called upon to help deal with reports of suspected errors and suggestions for additions or other modifications to the chapters. Often the Associate Editors are the original chapter authors, when they are available and willing to serve.</p> </div> <div id="p7" class="ltx_para"> <p class="ltx_p">The complete list of Editors, Senior Associate Editors, Associate Editors, and other currently active contributors to the DLMF Project are listed on the <a href=".././about/staff" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Staff</span></a> page. For acknowledgements of financial support see <a href=".././about/sponsors" title="In About the Project" class="ltx_ref"><span class="ltx_text ltx_ref_title">Funding</span></a>.</p> </div> </article> </div> <div class="ltx_page_footer"> <div class="ltx_siblings"> <a href=".././search/" title="" class="ltx_ref" rel="prev"><span class="ltx_text ltx_ref_title">Advanced Search</span></a><a href=".././about/notices" title="In About the Project" class="ltx_ref" rel="next"><span class="ltx_text ltx_ref_title">Notices</span></a> </div> <div class="ltx_footer_links ltx_centering"> <a href=".././about/notices">© 2010–2025 NIST</a> / <a href=".././about/notices#S2">Disclaimer</a> / <a href="mailto:DLMF-feedback@nist.gov">Feedback</a>; Version 1.2.4; Release date 2025-03-15.</div> <span id="pagesettings"></span> <div class="ltx_nist_logo"><a href="http://www.nist.gov/"><img src=".././style/nistidc.png" width="500" alt="NIST"></a></div> <div class="ltx_nist_links ltx_align_right"> <a href="https://www.nist.gov/privacy-policy">Site Privacy</a> <a href="https://www.nist.gov/oism/accessibility">Accessibility</a> <a href="https://www.nist.gov/privacy">Privacy Program</a> <a href="https://www.nist.gov/oism/copyrights">Copyrights</a> <a href="https://www.commerce.gov/vulnerability-disclosure-policy">Vulnerability Disclosure</a> <a href="https://www.nist.gov/no-fear-act-policy">No Fear Act Policy</a> <a href="https://www.nist.gov/foia">FOIA</a> <a href="https://www.nist.gov/environmental-policy-statement">Environmental Policy</a> <a href="https://www.nist.gov/summary-report-scientific-integrity">Scientific Integrity</a> <a href="https://www.nist.gov/nist-information-quality-standards">Information Quality Standards</a> <a href="https://www.commerce.gov/">Commerce.gov</a> <a href="http://www.science.gov/">Science.gov</a> <a href="http://www.usa.gov/">USA.gov</a> </div> </div> </div> </body> </html>