NIST Digital Library of Mathematical Functions (DLMF)

Calculation, Resources

Free
No Download/Install required
No registration

https://dlmf.nist.gov/

The NIST Digital Library of Mathematical Functions (DLMF) serves as the authoritative, peer-reviewed successor to the Abramowitz and Stegun Handbook of Mathematical Functions. It provides a comprehensive digital repository of mathematical formulas, identities, and properties for special functions used in advanced analysis. The site offers:

Rigorous definitions and notations for Bessel, Airy, and hypergeometric functions.
Interactive 3D visualizations and downloadable data for analyzing function behavior.
Extensive documentation of asymptotic expansions, recurrence relations, and numerical methods.

An incredible valuable math resource if not your specialty or rarely use some complex functions … of is years have passed since. The full, and more, content of a commercial expert book, without the price tag.

Tip: be ready to use the LaTeX format (use our dedicated posts and tools for LaTeX if not already familiar).

Standardize mathematical notation across large-scale, cross-disciplinary research projects.
Implement high-precision mathematical libraries in software development for scientific computing.
Verify the convergence and stability of specialized models used in manufacturing process optimization.

Disciplines: Applied mathematics, Physics, Engineering, Numerical analysis, Scientific computing.

Free alternative to Wolfram MathWorld, Abramowitz and Stegun, Wolfram Functions.

NIST Digital Library of Mathematical Functions compared with Wolfram MathWorld, Abramowitz and Stegun, and Wolfram Functions
NIST DLMF	Wolfram MathWorld	Abramowitz and Stegun	Wolfram Functions
Origin and authority: NIST released the DLMF online in 2010 as the successor to the 1964 handbook. About 50 external researchers contributed and NIST staff edited it. Cambridge University Press published a printed subset.	Origin and authority: Eric W. Weisstein created the site and largely wrote it, starting in 1995 from personal study notes. Wolfram Research sponsors it and holds a license to it.	Origin and authority: The handbook was published in 1964 by the National Bureau of Standards, now NIST, and edited by Milton Abramowitz and Irene Stegun. It runs to about 1,046 pages.	Origin and authority: The site belongs to Wolfram Research and presents itself as the largest formula compendium for mathematical functions on the web.
Content and form: The content covers special functions with interactive graphics, a math-based search engine, and links to references and software.	Content and form: It is an online encyclopedia covering a wide range of mathematics, not only special functions. It also appeared in print and on CD-ROM as the CRC Concise Encyclopedia of Mathematics.	Content and form: The handbook gives definitions, identities, approximations, plots and tables of values. NIST noted that more than half the pages were tables that are rarely needed with modern computers.	Content and form: Formulas are available in Wolfram Language StandardForm, MathML and ASCII, and the site shows how functions relate to each other. Wolfram Notebooks and PDF versions can be downloaded.
Licence and cost: NIST claims copyright over the DLMF, unlike the public-domain original handbook.	Licence and cost: Access is free. It returned to free public access in November 2001 after a legal dispute with CRC Press, which holds broad print rights.	Licence and cost: As a work of federal employees it is not protected by copyright in the United States. Several scans are online, and Dover issued a reprint.
	Accuracy and maintenance: The site is active and has been online since November 1999.	Accuracy and maintenance: Many printings added corrections, the tenth in 1972 among them, but some errata remain. A typo on page 886 spread into the name Bode rule for Boole rule.	Accuracy and maintenance: The About page says gaps in the content may point to areas needing further research.

Topics covered: NIST Digital Library, Mathematical Functions, Abramowitz and Stegun, Bessel functions, Airy functions, hypergeometric functions, asymptotic expansions, recurrence relations, numerical methods, interactive visualizations, mathematical notation, scientific computing, convergence, stability, software development, cross-disciplinary research, LaTeX, mathematical libraries, ISO 80000, ISO 31, ISO/IEC 25010, ISO 5725, and IEEE 754..