Abramowitz and Stegun


Abramowitz and Stegun is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards, now the National Institute of Standards and Technology. 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" on May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.

Overview

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:
  1. Mathematical Constants
  2. Physical Constants and Conversion Factors
  3. Elementary Analytical Methods
  4. Elementary Transcendental Functions
  5. Exponential Integral and Related Functions
  6. Gamma Function and Related Functions
  7. Error Function and Fresnel Integrals
  8. Legendre Functions
  9. Bessel Functions of Integral Order
  10. Bessel Functions of Fractional Order
  11. Integrals of Bessel Functions
  12. Struve Functions and Related Functions
  13. Confluent Hypergeometric Functions
  14. Coulomb Wave Functions
  15. Hypergeometric Functions
  16. Jacobian Elliptic Functions and Theta Functions
  17. Elliptic Integrals
  18. Weierstrass Elliptic and Related Functions
  19. Parabolic Cylinder Functions
  20. Mathieu Functions
  21. Spheroidal Wave Functions
  22. Orthogonal Polynomials
  23. Bernoulli and Euler Polynomials, Riemann Zeta Function
  24. Combinatorial Analysis
  25. Numerical Interpolation, Differentiation, and Integration
  26. Probability Functions
  27. Miscellaneous Functions
  28. Scales of Notation
  29. Laplace Transforms

    Editions

Because the Handbook is the work of U.S. federal government employees acting in their official capacity, it is not protected by copyright in the United States. While it could be ordered from the Government Printing Office, it has also been reprinted by commercial publishers, most notably Dover Publications, and can be legally viewed on and downloaded from the web.
While there was only one edition of the work, it went through many print runs including a growing number of corrections.
Original NBS edition:
Reprint edition by Dover Publications:
and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas, but reducing the numerical tables to a minimum, which, by this time, could be easily calculated with scientific pocket calculators. The references were removed as well. Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter. The numbering of formulas was kept for easier cross-reference.
A digital successor to the Handbook, long under development at NIST, was released as the “Digital Library of Mathematical Functions” on May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.