This update includes several corrections, clarifications and updates.(seeVersion 1.2.4 (March 15, 2025) for details).

This update includes several corrections, clarifications and updates.(seeVersion 1.2.3 (December 15, 2024) for details).

This update includes several corrections, clarifications and updates.(seeVersion 1.2.2 (September 15, 2024) for details).

We regret having to report that Barry Schneider passed away on July 3, 2024.Please seeBarry I. Schneider for a tribute and obituary.

We are happy to report that several individuals have agreed to act as AssociateEditor for DLMF chapters.Victor H. Moll will act as Associated Editor for DLMF Chapters20,23.Gergő Nemes will act as Associate Editor for DLMF Chapters5,8,9,10,11.Joris Van der Jeugt will act as Associate Editor forChapter34.Hans Volkmer will act as Associate Editor for DLMF Chapters22,28,29,30,31.

This update includes several corrections and clarifications.(seeVersion 1.2.1 (June 15, 2024) for details).

On advice of the senior associate editors it was decided in 2016 toexpand Chapter18 (Orthogonal Polynomials (OP)). Most sections wereenlarged including the sections on associated OP’s, Pollaczekpolynomials and physical applications. To help the users of the DLMFit was decided that much more information should be given in thesection on general OP’s, and as a consequence Chapter1(Algebraic and Analytic Methods) did need a significant expansion,especially more information on matrix analysis, measure theory, spectralanalysis, and a new section on linear second order differential operatorsand eigenfunction expansions. This release increments the minor versionnumber and contains considerable additions of new material andclarifications (seeVersion 1.2.0 (March 27, 2024) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.12 (December 15, 2023) for details).

We regret having to report that Diego Dominici passed away on October 16, 2023.Please seeDiego Dominici for a tribute and obituary.

This update includes several corrections and clarifications.(seeVersion 1.1.11 (September 15, 2023) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.10 (June 15, 2023) for details).

We regret having to report that Brian R. Judd passed away on April 8, 2023.Please seeBrian R. Judd for an update.

We regret having to report that Ross R. Barnett passed away on November 21, 2018.Please seeAntony Ross Barnett for an update.

This update includes several corrections and clarifications.(seeVersion 1.1.9 (March 15, 2023) for details).

DLMF now uses browser-native MathML rendering for mathematics, by default,in all browsers which support MathML.SeeAbout MathML for more details and for other options.

This update includes several corrections and clarifications.(seeVersion 1.1.8 (December 15, 2022) for details).Our mathematics markup now conforms with the MathML Core specification and should be acceptablein most browsers (current Firefox, Safari and the upcoming Chrome release;seeAbout MathML for details).

We regret having to report that Richard B. Paris passed away on July 8, 2022.Please seeRichard B. Paris for a tribute and obituary.

This update includes enhanced coverage of the Lambert$W$-functionalong with other corrections and clarifications.(seeVersion 1.1.7 (October 15, 2022) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.6 (June 30, 2022) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.5 (March 15, 2022) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.4 (January 15, 2022) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.3 (September 15, 2021) for details).

We regret having to report that Brian D. Sleeman passed away on July 19, 2021.Please seeBrian D. Sleeman for a tribute and obituary.

This update includes several corrections and clarifications.(seeVersion 1.1.2 (June 15, 2021) for details).

This update includes several corrections and clarifications.(seeVersion 1.1.1 (March 15, 2021) for details).

This release increments the minor version numberand contains considerable additions of new material and clarifications.These additions were facilitated by an extension of the scheme for reference numbers.(seeVersion 1.1.0 (December 15, 2020) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.28 (September 15, 2020) for details).

We regret having to report that Ranjan Roy passed away on August 12, 2020.Please seeRanjan Roy for an update.

This update includes several corrections and clarifications.(seeVersion 1.0.27 (June 15, 2020) for details).

We regret having to report that Leonard C. Maximon passed away on January 4, 2020.Please seeLeonard C. Maximon for an update.

This update includes several corrections and clarifications.(seeVersion 1.0.26 (March 15, 2020) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.25 (December 15, 2019) for details).

We regret having to report that Richard A. Askey passed away on October 9, 2019.Please seeRichard A. Askey for a tribute and obituary.

This update includes several corrections and clarifications.(seeVersion 1.0.24 (September 15, 2019) for details).

The editorial board was expanded to includeHoward S. Cohl as Technical Editor andMarjorie A. McClain as Associate Technical Editor.

This update includes several corrections and clarifications.(seeVersion 1.0.23 (June 15, 2019) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.22 (March 15, 2019) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.21 (December 15, 2018) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.20 (September 15, 2018) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.19 (June 22, 2018) for details).

We regret having to report that Philip J. Davis passed away on March 14, 2018.Please seePhilip J. Davis for a tribute and obituary.

This update includes several corrections and clarifications.(seeVersion 1.0.18 (March 27, 2018) for details).

This update includes several corrections and clarifications.(seeVersion 1.0.17 (December 22, 2017) for details).

We regret having to report that Tom M. Apostol passed away on May 8, 2016.Please seeTom M. Apostol for an update.

This update includes several corrections and clarifications.(seeVersion 1.0.16 (September 18, 2017) for details).

This update includes the addition of a new subsection, a change of notationfor integral transforms and other clarifications. The graphical decorations,icons and mouse-cursors were freshened to improve interaction and updated to SVG.(seeVersion 1.0.15 (June 1, 2017) for details).

This update includes another set of corrections caught by our readers,improvements in notation and additional citations and clarifications.(seeVersion 1.0.14 (December 21, 2016) for details).

This update includes just a single item; a fix was made to a typographical error made in (13.9.16).(seeVersion 1.0.13 (September 16, 2016) for details).

This update includes another set of corrections caught by our readers,improvements in notation and additional citations and clarifications.(seeVersion 1.0.12 (September 9, 2016) for details).We’ve also updated ourHow to Cite recommendations.

The Editors of the NIST Digital Library of Mathematical Functions havebegun to consider how current content can be improved or enlarged.Input from the community is quite welcome as we begin this process.Please send your thoughts toDLMF Feedback.

This update includes some small additions, some corrections caught by our readers,improvements in notation and additional citations and clarifications.(seeVersion 1.0.11 (June 8, 2016) for details).

Not mentioned in the previous news item was two new features:List of Figures andList of Tables.

This update includes some corrections caught by our readers,improvements in notation and additional citations and clarifications.(seeVersion 1.0.10 (August 7, 2015) for details).

Version 1.0 (beta) of the DLMF Standard Reference Tables web service (DLMF Tables) has been released. Its goal is to provide a standard of comparison for testing numerical software by computing, on demand, values of selected special functions to user-defined precision with guaranteed error bounds.

DLMF Tables has the following features:

1. 1.

   arguments are read from web form or uploaded file;

2. 2.

   user-specified precision (up to 500 digits);

3. 3.

   computation errors (truncation and rounding) are analyzeda priori to satisfy the required accuracy;

4. 4.

   provides strict high-precision enclosures (upper/lower bounds);

5. 5.

   optional round to nearest or directed roundings;

6. 6.

   comparison to user-supplied function values, highlightingany differences and providing approximate relative errors;

7. 7.

   links to function definitions inhttp://dlmf.nist.gov/, the NIST Digital Library of Mathematical Functions.

DLMF Tables is available athttp://dlmftables.uantwerpen.be/

It is a result of collaboration between the NIST Applied and Computational Mathematics Division and the University of Antwerp Computational Mathematics Research Group. Any comments on the new service will be gratefully received atDLMFTables Feedback.

This update includes a few corrections caught by our readers,improvements in notation and additional citations and clarifications(seeVersion 1.0.9 (August 29, 2014) for details).

This update includes corrections caught by our readers,along with a few clarifications (seeVersion 1.0.8 (April 25, 2014) for details).

We also changed the characters previously used for exponential e, imaginary i and differential d,from special Unicode characters, which were not always available locally for useby browsers, to normal characters. In addition, some minor changes to pagelayouts have been implemented.

The editorial board was expanded to includeBarry I. Schneider as AssociateGeneral Editor,Bruce R. Miller as Information Technology Editor andBonita V. Saunders as Visualization Editor.

This significant update enhances the accessibility,portability and usability of DLMF:

• New Feature:

  The default document format is now HTML5 which includes MathMLproviding better accessibility and display of mathematics.SeeBrowsers for more informationand solutions to potential problems.

• New Feature:

  All interactive 3D graphics have been recast using WebGL and X3DOM, which is now the default format.This improves portability and performance;It is now possible to interactively rotate, scale and explore function surfaceswithout downloading a special plugin.An example can be seen atFigure 5.3.4.

  SeeViewing DLMF Interactive 3D Graphics for more informationand solutions to potential problems.

• –

  Additionally, several errata and clarifications have been made(seeVersion 1.0.7 (March 21, 2014) for details).

We regret reporting that Bille C. Carlson passed away on August 16.Please seeBille C. Carlson for an obituary.

We are very sad to report that Frank W. J. Olver passed awayon April 23.Please seeFrank W. J. Olver for a tribute and obituary.

This minor update improves rendering in various ways,primarily tracking changes to underlying theLaTeXML system.

This update includes several corrections caught by our readers,along with a number of clarifications and small additions ofuseful additional material (seeVersion 1.0.5 (October 1, 2012) for details).The suggestions atHow to Cite should be more useful,and sample BibTeX entries are now provided.Additionally, the production process has improved the fidelityof the web conversion, resulting in better layoutand presentation of math.

We have reports of problems with MathML displaywhen using MathPlayer 2.2 with IE9.Previous versions, such as IE8, seem to work well.The beta version 3 of MathPlayer should work better;please monitor Design Science’sMathPlayer pluginpages for information about updates.

As a last resort, recall that you can choosetheHTML+images format in theCustomize DLMF page— although we would hope this need only be a temporary measure.

This minor update improves rendering of math (particularly continued fractions and line-breaks)and graphics (some diagrams and larger VRML) in several places,as well as enhancements to navigation and additions to the software index.Updated information about VRML and 3D browsers is available; seeViewing DLMF Interactive 3D Graphics.

The NIST Digital Library of Mathematical Functions was selected for recognition as anOutstanding Information Technology Achievement in Government for 2011 by GovernmentComputer News (GCN). According to GCN, these awards “have come to symbolize the bestand most notable IT accomplishments in advancing the work of government agencies.”Ten projects were selected for recognition this year from more than 200 nominations.The selection was based on “the degree of innovation in the technology plan carried out,the quality of the leadership that carried the project to fruition,”and “the degree to which a given IT project improved an agency’s ability tooperate more efficiently or serve the public more effectively”.Other awardees this year include an app from the City of Boston that enablescitizens to request city services from their smartphones and the IT infrastructurethat supports the TSA’s secure flight program.NIST staff members cited for thisachievement are Daniel Lozier, Frank Olver, Ronald Boisvert, Bruce Miller,Bonita Saunders, Marjorie McClain, Abdou Youssef, Qiming Wang, Brian Antonishek,and Charles Clark. The project team was formally honored at the 24th Annual GCNAwards Gala, October 19, 2011 at the Ritz-Carlton, Tysons Corner in McLean, Va.For further information seehttp://gcn.com/articles/2011/08/05/2011-gcn-award-winners.aspx?sc_lang=enandhttp://gcn.com/articles/2011/10/17/nist-math-handbook-profile-main.aspx.

This update makes some clarifications (seeVersion 1.0.3 (Aug 29, 2011) for details),along with other minor modifications to the online version:additions to the software index (seeSoftware Index);updated help files;a correction to the VRML phase coloring for22.3.24;and improved associations between notations described inMathematical Introduction and their usages.

We are pleased to acknowledge native support for MathML in Version 5.1 of the Safari web browser!While it is an excellent initial implementation, it omits support for themmultiscripts element— a critical element for presenting hypergeometric functions.

To avoid confusion, we regret not yet delivering MathML to Safari browsers, by default.In the meantime, those Safari users who wish to experiment with MathML mayenable it by checkingXHTML+MathML for ‘Document Format’ atCustomize DLMF;the use of STIX fonts is also encouraged (SeeSpecial fonts for MathML).

We will continue to monitor Safari development.

A quick followup improves rendering in several places, particularly for InternetExplorer;the help pages were revised.

We are proud to announce an update of the DLMF to version 1.0.1which corrects a number of issues:

• –

  A small number of errors and clarifications were made,seeVersion 1.0.1 (June 27, 2011) for details;

• –

  The listings of available software for special functionshave been updated, seeSoftware Index for details

• –

  Several improvements were made to the document conversion,layout and presentation.

The just-released version 4 of Firefox fixes a disturbing MathML display bug.Previously, unless STIX fonts were installed, the surd for the square root of a fractionwould not stretch enough to cover both the numerator and denominator.This caused, for example, the first square root within the parentheses in8.11.12to look likesqrt(pi)/2 rather thansqrt(pi/2).(SeeMozilla Bug 454155).

Users of Firefox before version 4 should upgrade; when thatis not possible, installing the STIX fonts is recommended (SeeSpecial fonts for MathML).

[Incidentally, such rendering errors can easily be verified by comparingthe displayed MathML to the sourceTeX code or the png image of the formula whichcan be found under ‘Encoding’ in the ‘info box’ (hover over or click thesymbol next to every numbered formula)].

We are proud to announce the public availability of theDigital Library of Mathematical Functionsas well as the publishing of theNIST Handbook of Mathematical FunctionsbyCambridge University Press, effective this date.

There appears to be a performance regression for Firefoxversions 3.6.x when running under some versions of Windows,causing complex pages with large amounts of MathML — such as ours — to display very slowly.This problem is fixed in version 3.6.9 and later(SeeMozilla Bug 564309).

Cambridge University Press has been selected as publisher for the handbookversion of the NIST Digital Library of Mathematical Functions (DLMF). Thisselection was made by evaluating and ranking several proposals that responded tothe publicly announced request for proposals and were received by the deadline.

Final preparation of the handbook and Web versions is in process. Theapproximately simultaneous publication of the handbook and release of the Website will occur in late 2009 or early 2010.

The National Institute of Standards and Technology (NIST) seeksproposals from publishers interested in licensing the rights toproduce and market a printed version of the NIST Digital Libraryof Mathematical Functions (DLMF).For complete information seePublic Announcement.

Clarifications:

For the 3D graphics in the book, do they require 3D glasses?

No. Although an interesting idea, there is no consideration ofspecial viewing aids for the book version of the DLMF.

If all the material in the book will be on the web, do youreally want to add the expense of a DVD to the book?

Please understand that the DVD (or other suitable media,such as CD) will contain only PDF files of the book version of theDLMF. There is no intention to reproduce the Web version fordistribution with the book. The Web version will be accessiblefrom the NIST DLMF website and, potentially, from NIST-authorizedmirror sites.

What is the total number of figures and the total number ofcolor figures? Ballpark figures are fine.

By a recent approximate count, there are 409 figures. Of these,347 include color. The 3D surfaces with continuous color accountfor 140 of the color figures; 2D line graphs and diagrams withsolid-colored lines account for the remainder.

On page 5 of the Public Announcement, it’s stated, underInitial Production, that a proposal for a cover design is requiredand is to be based on the Sample Chapter Collection. The deliverydate for the cover design is to be included in the ProductionPlan. Does this mean a draft design based on the Sample isrequired as part of the solicitation process?

No. The purpose of the itemized lists on pages 5 and 6 is todescribe the essential elements of the license agreement that willbe drawn up by NIST and the selected licensee. The proposal forcover design is required after a licensee has been selected as aresult of the solicitation process. Only the delivery date of thecover design proposal is required now. This date can be indicated,for example, as “xxx days after notification of selection by NIST”.