# Digital Library of Mathematical Functions

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{{Short description|Online collection of special functions from NIST}}
{{Use dmy dates|date=June 2019|cs1-dates=y}}
{{Use list-defined references|date=December 2021}}
The '''Digital Library of Mathematical Functions''' ('''DLMF''') is an online project at the [National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology) (NIST) to develop a database of mathematical reference data for [special functions](/source/special_functions) and their applications. It is intended as an update of ''[Abramowitz's and Stegun's Handbook of Mathematical Functions](/source/Abramowitz_and_Stegun)'' (A&S).<ref name="Boisvert_2011"/> It was published online<ref name="Online"/> on 7 May 2010, though some chapters appeared earlier. In the same year it appeared at [Cambridge University Press](/source/Cambridge_University_Press) under the title '''''NIST Handbook of Mathematical Functions'''''.<ref name="NIST_2010"/>

In contrast to A&S, whose initial print run was done by the [U.S. Government Printing Office](/source/U.S._Government_Printing_Office) and was in the [public domain](/source/public_domain), NIST asserts that it holds copyright to the DLMF under [Title 17 USC 105](/source/Copyright_status_of_work_by_the_U.S._government) of the U.S. Code.<ref name="DLMF Notices"/>

==See also==
* [NIST Dictionary of Algorithms and Data Structures](/source/NIST_Dictionary_of_Algorithms_and_Data_Structures)

==References==
<references>
<ref name="Boisvert_2011">{{cite journal |author-last1=Boisvert |author-first1=Ronald F. |author-first2=Charles W. |author-last2=Clark |author-first3=Daniel W. |author-last3=Lozier |author-first4=Frank William John |author-last4=Olver |author-link4=Frank William John Olver |title=A Special Functions Handbook for the Digital Age |journal=[Notices of the American Mathematical Society](/source/Notices_of_the_American_Mathematical_Society) |volume=58 |issue=7 |date=2011 |pages=905–911 |url=https://www.ams.org/notices/201107/rtx110700905p.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144026/https://www.ams.org/notices/201107/rtx110700905p.pdf |archive-date=2021-09-09}}</ref>
<ref name="Online">{{cite web|url=https://dlmf.nist.gov/|title=NIST Digital Library of Mathematical Functions|publisher=[National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology) (NIST)|access-date=July 24, 2023}}</ref>
<ref name="NIST_2010">{{cite book |title=NIST Handbook of Mathematical Functions |editor1-first=Frank William John |editor1-last=Olver |editor1-link=Frank William John Olver |editor2-first=Daniel W. |editor2-last=Lozier |editor3-first=Ronald F. |editor3-last=Boisvert |editor4-first=Charles W. |editor4-last=Clark |date=2010 |publisher=[National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology) (NIST), [U.S. Department of Commerce](/source/U.S._Department_of_Commerce), [Cambridge University Press](/source/Cambridge_University_Press) |isbn=978-0-521-19225-5 |mr=2723248}} [http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521140638]</ref>
<ref name="DLMF Notices">{{cite web  |url=https://dlmf.nist.gov/about/notices |title=DLMF: Notices |publisher=NIST |access-date=2010-12-28}}</ref>
</references>

==Further reading==
* {{cite web |author-last=Cipra |author-first=Barry Arthur |author-link=Barry Arthur Cipra |title=A New Testament for Special Functions? |work=[SIAM News](/source/SIAM_News) |publisher=[SIAM](/source/SIAM) |date=1998-03-08 |url=http://www.siam.org/news/news.php?id=819 |url-status=dead |archive-url=https://web.archive.org/web/20070715154809/http://www.siam.org/news/news.php?id=819 |archive-date=2007-07-15}}
* {{cite web |author-last=Lozier |author-first=Daniel W. |title=Toward a Revised NBS Handbook of Mathematical Functions |publisher=[National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology) (NIST) |id=NIST<span title="Interagency Report">IR</span> 6072 |date=October 1997 |pages=2089–9 |orig-date=September 1997 |citeseerx=10.1.1.65.5096 |url=https://www.researchgate.net/profile/Daniel-Lozier/publication/228544356_Toward_a_revised_NBS_handbook_of_mathematical_functions/links/00b495319e8b15ddea000000/Toward-a-revised-NBS-handbook-of-mathematical-functions.pdf<!-- https://www.researchgate.net/publication/228544356 --> |url-status=live |archive-url=https://web.archive.org/web/20211228141848/https://www.researchgate.net/profile/Daniel-Lozier/publication/228544356_Toward_a_revised_NBS_handbook_of_mathematical_functions/links/00b495319e8b15ddea000000/Toward-a-revised-NBS-handbook-of-mathematical-functions.pdf |archive-date=2021-12-28}} [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.65.5096&rep=rep1&type=pdf] (8 pages)
* {{cite web |title=NIST Releases Preview of Much-Anticipated Online Mathematics Reference |date=2008-06-27 |publisher=[ScienceDaily](/source/ScienceDaily) |url=https://www.sciencedaily.com/releases/2008/06/080627163210.htm |access-date=2021-12-28 |url-status=live |archive-url=https://web.archive.org/web/20210211010422/http://www.sciencedaily.com/releases/2008/06/080627163210.htm |archive-date=2021-02-11}}
* {{cite web |title=Birth of a Classic … Take Two |date=2010-05-11 |publisher=[National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology), [United States Department of Commerce](/source/United_States_Department_of_Commerce) |type=Video |url=https://www.youtube.com/watch?v=Exf02R1FnXY |url-status=live |archive-url=https://ghostarchive.org/varchive/youtube/20211221/Exf02R1FnXY |archive-date=2021-12-21}}{{cbignore}}

==External links==
* [https://dlmf.nist.gov NIST Digital Library of Mathematical Functions]
* [http://dlmf.nist.gov/errata/ Corrected errors in NIST DLMF]

Category:Handbooks and manuals
Category:Mathematics websites
Category:Mathematical tables
Category:Numerical analysis
Category:Special functions
Category:Mathematical databases

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Adapted from the Wikipedia article [Digital Library of Mathematical Functions](https://en.wikipedia.org/wiki/Digital_Library_of_Mathematical_Functions) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Digital_Library_of_Mathematical_Functions?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.