Abramowitz and Stegun

Abramowitz and Stegun
M. Abramowitz and I.A. Stegun · Public domain · source
Name	Handbook of Mathematical Functions
Author	Milton Abramowitz; Irene A. Stegun (eds.)
Country	United States
Language	English
Subject	Mathematical functions
Publisher	National Bureau of Standards
Pub date	1964
Media type	Print
Pages	1046

Contents

Abramowitz and Stegun is the informal name for the Handbook of Mathematical Functions edited by Milton Abramowitz and Irene A. Stegun, a comprehensive reference for special functions, numerical methods, and tables. First published by the National Bureau of Standards in 1964, the work became a standard reference for practitioners associated with National Physical Laboratory (United Kingdom), Argonne National Laboratory, Los Alamos National Laboratory, Princeton University, Massachusetts Institute of Technology, and other institutions. The handbook aggregated results connected to figures such as Leonhard Euler, Carl Friedrich Gauss, Niels Henrik Abel, Srinivasa Ramanujan, and Adrien-Marie Legendre, and it influenced computational projects at Bell Labs, IBM, Harvard University, Stanford University, and California Institute of Technology.

Background and Publication

The project originated within the National Bureau of Standards and drew on earlier compendia like works by George Boole, Arthur Cayley, and monographs from G. H. Hardy and E. T. Whittaker. Editors Abramowitz and Stegun coordinated contributions from specialists with ties to University of Chicago, University of Cambridge, University of Göttingen, University of Oxford, and École Normale Supérieure. The editorial process paralleled efforts at Royal Society publishing and mirrored data-gathering methods used by U.S. Army, U.S. Navy, and Department of Defense research programs. Publication was timed alongside computational advances at ENIAC, UNIVAC, and the IBM 701, responding to demands from projects like Manhattan Project, Apollo program, and numerical analysis tasks at National Aeronautics and Space Administration. The handbook appeared during the Cold War era with contemporaneous scientific activity at Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Oak Ridge National Laboratory.

The handbook is organized into chapters covering gamma functions, Bessel functions, elliptic integrals, orthogonal polynomials, and asymptotic expansions. It includes tables, graphs, and formulae associated with authorities such as Augustin-Louis Cauchy, Joseph Fourier, Pierre-Simon Laplace, Siméon Denis Poisson, and James Clerk Maxwell. Each chapter cites classical sources including works by Bernhard Riemann, Friedrich Bessel, Carl Gustav Jacobi, Sophie Germain, and Adrien-Marie Legendre. Numerical methods treatments reference contributions from John von Neumann, Alan Turing, Doron Zeilberger, and algorithms used at Brookhaven National Laboratory and CERN. Indexing and cross-referencing echo cataloging systems employed by Library of Congress, British Library, and Deutsche Nationalbibliothek.

The handbook served applied researchers in fields associated with Richard Feynman, Werner Heisenberg, Enrico Fermi, and Paul Dirac by consolidating results for special functions used in quantum mechanics, electrodynamics, and statistical mechanics. It underpinned computational work in disciplines represented at Princeton Plasma Physics Laboratory, Max Planck Institute, and Salk Institute and informed models developed at Bell Labs, AT&T, General Electric Research Laboratory, and Siemens. Engineers working on signal processing, radar, and acoustics referenced material relevant to projects at Raytheon, Northrop Grumman, Boeing, and Lockheed Martin. Mathematicians influenced by the handbook included researchers connected to Institute for Advanced Study, Courant Institute, Mathematical Association of America, and American Mathematical Society. Applications ranged from computations in the Navier–Stokes equations context to analyses appearing in publications from Physical Review, Proceedings of the Royal Society, and Annals of Mathematics.

Abramowitz and Stegun's handbook catalyzed successors such as the NIST Digital Library of Mathematical Functions, software libraries like Fortran Numerical Recipes, GNU Scientific Library, Boost C++ Libraries, and symbolic systems from Wolfram Research, Maplesoft, and SageMath. It influenced standards at International Organization for Standardization and curricula at institutions including Yale University, Columbia University, Cornell University, University of California, Berkeley, and Imperial College London. The handbook's tables were digitized in projects at National Institute of Standards and Technology, Google, and Internet Archive, while scholars at Princeton University Press and Cambridge University Press drew on its structure for later reference works. Its role in computational practice linked it historically to pioneers such as G. H. Hardy, Norbert Wiener, Hermann Weyl, and Ludwig Prandtl.

The original 1964 edition was distributed by the U.S. Government Printing Office and reprinted in various forms; translations and adapted editions circulated through publishers in France, Germany, Japan, Russia, and China. Digital successors and scanned editions are available through initiatives at National Institute of Standards and Technology, Smithsonian Institution, and archival services at Library of Congress. Accessibility efforts connected with projects at Open Knowledge Foundation and Project Gutenberg have promoted preservation, while computational implementations appear in repositories maintained by GitHub and mirror sites used by European Organization for Nuclear Research. The handbook remains categorized within historical collections at Cornell University Library, Harvard Library, and New York Public Library.

Category:Mathematical reference works