Concept
Abramowitz and Stegun (AS) is the informal name of a 1964 mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. A digital successor to the Handbook was released as the "Digital Library of Mathematical Functions" (DLMF) on 11 May 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press. Since it was first published in 1964, the 1046 page Handbook has been one of the most comprehensive sources of information on special functions, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of applied mathematics. The notation used in the Handbook is the de facto standard for much of applied mathematics today. At the time of its publication, the Handbook was an essential resource for practitioners. Nowadays, computer algebra systems have replaced the function tables, but the Handbook remains an important reference source. The foreword discusses a meeting in 1954 in which it was agreed that "the advent of high-speed computing equipment changed the task of table making but definitely did not remove the need for tables". The chapters are: Mathematical Constants Physical Constants and Conversion Factors Elementary Analytical Methods Elementary Transcendental Functions Exponential Integral and Related Functions Gamma Function and Related Functions Error Function and Fresnel Integrals Legendre Functions Bessel Functions of Integral Order Bessel Functions of Fractional Order Integrals of Bessel Functions Struve Functions and Related Functions Confluent Hypergeometric Functions Coulomb Wave Functions Hypergeometric Functions Jacobian Elliptic Functions and Theta Functions Elliptic Integrals Weierstrass Elliptic and Related Functions Parabolic Cylinder Functions Mathieu Functions Spheroidal Wave Functions Orthogonal Polynomials Bernoulli and Euler Polynomials, Riemann Zeta Function Combinatorial Analysis Numerical Interpolation, Differentiation, and Integration Probability Functions Miscellaneous Functions Scales of Notation Laplace Transforms Because the Handbook is the work of U.
