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DLMF: Digital Library of Mathematical Functions

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Digital Library of Mathematical Functions


Abramowitz and Stegun's Handbook of Mathematical Functions (with Formulas, Graphs, and Mathematical Tables) was first published by the National Bureau of Standards in 1964. It remains a technical best-seller and is among the most widely cited of all math reference compendia.
But the Handbook is increasingly out-of-date. A project is underway at the National Institute of Standards and Technology (the heir to NBS) to develop a replacement which will become a major resource of math reference data for special functions and their applications.
 

The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology to develop a major resource of math reference data for special functions and their applications. It is intended as an update of the Handbook of mathematical functions. As of summer 2007, the chapter on the Gamma function is available online, and the remaining chapters are expected to appear soon.
 

Abramowitz and Stegun's Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables is being completely rewritten with regard to the needs of today. The new DLMF (Digital Library of Mathematical Functions) will appear in a hardcover edition and as a free electronic publication on the World Wide Web. The authors will review the relevant published literature and produce approximately twice the number of formulas that were contained in the original Handboook. The DLMF will make full use of advanced communications and computational resources to present downloadable math data, manipulable graphs, tables of numerical values, and math-aware search. The authoritative status of the existing Handbook, and its orientation toward applications in science, statistics, engineering and computation, will be preserved.

Thus the utilitarian value of the Handbook will be extended far beyond its original scope and the traditional limitations of printed media. The term digital library has gained acceptance for this kind of information resource, and the choice of project title reflects the hope that the DLMF will be a vehicle for revolutionizing the way applicable mathematics in general is practiced and delivered.
 

Table of Contents of Digital Library of Mathematical Functions
AL Algebraic and Analytic Methods
AS Asymptotic Approximations
NM Numerical Methods
EF Elementary Functions
GA Gamma Function
EX Exponential Integral, Logarithmic Integral, Sine and Cosine Integrals
ER Error Functions, Dawson's Integral, and Fresnel Integrals
IG Incomplete Gamma and Related Functions
AI Airy and Related Functions
BS Bessel Functions
ST Struve and Related Functions
CH Confluent Hypergeometric Functions
PC Parabolic Cylinder Functions
LE Legendre Functions and Associated Legendre Functions
HY Hypergeometric Function
GH Generalized Hypergeometric Functions and Meijer G-Function
QH q-Hypergeometric Functions
OP Orthogonal Polynomials
EL Elliptic Integrals
TH Theta Functions
MT Riemann Theta Functions
JA Jacobian Elliptic Functions
WE Weierstrass Elliptic and Modular Functions
BP Bernoulli and Euler Numbers and Polynomials
ZE Zeta and Related Functions
NT Functions of Number Theory
CM Combinatorial Analysis
MA Mathieu Functions and Hill's Equation
LA Lamé Functions
SW Spheroidal Wave Functions
HE Heun Functions
PT Painlevé Transcendents
FM Functions of Matrix Argument
CW Coulomb Wave Functions
TJ 3j, 6j, 9j Symbols
IC Integrals with Coalescing Saddles
SM Statistical Methods & Distributions
CA Computer Algebra

 

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