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The NIST Digital Library of Mathematical Functions: A 21st Century Source of Information on the Special Functions of Mathematical Physics



Barry I. Schneider, Bruce R. Miller, Bonita V. Saunders


In 1964 the National Bureau of Standards (NBS) published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, AMS 55, edited by Milton Abramowitz and Irene A. Stegun. This handbook satisfied an important and largely unfulfilled need; to provide the scientific and engineering community a single place to easily find information on the important functions of mathematical physics. That publication became the most widely distributed and cited NBS (now National Institute of Standards and Technology (NIST)) publication in the first 100 years of the institution’s existence. It proved to be an invaluable reference for physicists and other scientists and engineers who use the special functions of applied mathematics in their day-to-day work. The success of the original handbook, widely referred to as ‘Abramowitz and Stegun’, or simply ‘A&S’, derived from the fact that it provided critically useful mathematical data in a concise format. The objective was usability to scientists and engineers in their day-to-day work, not proofs of mathematical formulas for mathematicians. In 1998, a project was initiated to develop a new printed handbook as well as a freely accessible on-line version to take advantage of the relatively new potential of the World Wide Web and to update the mathematical content to the new millenium. This article is devoted to describing the DLMF and its potential for enabling physicists seeking information on the special functions for their research to easily find and effectively use the new resource.
Physics Today


Special functions, digital library of mathematical functions, mathematical properties of functions
Created January 1, 2018, Updated May 15, 2020