Abramowitz and Stegun

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Short description: 1964 mathematical reference work edited by M. Abramowitz and I. Stegun

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
Handbook of Mathematical Functions, by Abramowitz and Stegun, cover.jpg
Cover of the ninth printing, 1970
AuthorMilton Abramowitz and Irene Stegun
CountryUnited States
LanguageEnglish
GenreMath
PublisherUnited States Department of Commerce, National Bureau of Standards (NBS)
Publication date
1964
ISBNISBN:0-486-61272-4
OCLC18003605

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 .[1]

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.[2][3][4] 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".

More than 1,000 pages long, the Handbook of Mathematical Functions was first published in 1964 and reprinted many times, with yet another reprint in 1999. Its influence on science and engineering is evidenced by its popularity. In fact, when New Scientist magazine recently asked some of the world's leading scientists what single book they would want if stranded on a desert island, one distinguished British physicist[5] said he would take the Handbook.

The Handbook is likely the most widely distributed and most cited NIST technical publication of all time. Government sales exceed 150,000 copies, and an estimated three times as many have been reprinted and sold by commercial publishers since 1965. During the mid-1990s, the book was cited every 1.5 hours of each working day. And its influence will persist as it is currently being updated in digital format by NIST.

– NIST[6]

right|thumb|Page 97 showing part of a table of common logarithms

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 (ISBN:0-486-61272-4), 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:

  • 1st printing: June 1964; errata:[7][8][9][10][11][12][13][nb 1]
  • 2nd printing with corrections: November 1964; errata:[11][nb 1]
  • 3rd printing with corrections: March 1965; errata:[11][13][nb 1]
  • 4th printing with corrections: December 1965; errata:[11][13][nb 1]
  • 5th printing with corrections: August 1966
  • 6th printing with corrections: November 1967
  • 7th printing with corrections: May 1968
  • 8th printing with corrections: 1969
  • 9th printing with corrections: November 1970
  • 10th printing with corrections: December 1972[nb 1]

Reprint edition by Dover Publications:

  • 1st printing: 1965[2]
  • ?
  • 9th printing with additional corrections (based on 10th printing of NBS edition with corrections)[nb 1]

Related projects

Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984.[14][15] The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum,[14] which, by this time, could be easily calculated with scientific pocket calculators.[15] The references were removed as well.[15] Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter.[15] The numbering of formulas was kept for easier cross-reference.[15]

A digital successor to the Handbook, long under development at NIST, 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 .[1]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Cite error: Invalid <ref> tag; no text was provided for refs named NB_Errata
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References

  1. ↑ 1.0 1.1 NIST Handbook of Mathematical Functions. National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Cambridge University Press. 2010. ISBN 978-0-521-19225-5.  [1]
  2. ↑ 2.0 2.1 "Abramowitz, M., And I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications, Inc., 1965, 1046 pp., $4.50 (paperback)". Management Science 14 (6 (#2)): B-404. February 1968. https://ur.booksc.eu/book/59644937/4c5eeb. Retrieved 2021-12-31. 
  3. ↑ "Reviews and Descriptions of Tables and Books 1: Milton Abramowitz & Irene A. Stegun, Editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964, xiv + 1046p., 27 cm. Price $6.50.". Mathematics of Computation 19 (89): 147–149. April 1965. doi:10.2307/2004114. MSC:A-F,H-M,R,SX. ISSN 0025-5718. https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf. Retrieved 2016-03-13. 
  4. ↑ "A Special Functions Handbook for the Digital Age". Notices of the American Mathematical Society (NAMS) 58 (7): 905–911. 2011. https://www.ams.org/notices/201107/rtx110700905p.pdf. Retrieved 2016-03-13. 
  5. ↑ "Christmas books: ... Or maybe two or three ...". New Scientist. 1997-11-22. https://www.newscientist.com/article/mg15621095.500-christmas-books-----or-maybe-two-or-three---.html. Retrieved 2016-03-13.  [2]
  6. ↑ "NIST at 100: Foundations for Progress, 1964: Mathematics Handbook Becomes Best Seller". 2001. https://www.nist.gov/centennial/ph_spaceage.cfm#1964. 
  7. ↑ "Table Errata 362: Milton Abramowitz & Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, No. 55, U. S. Government Printing Office, Washington, D. C., 1964.". Mathematics of Computation 19 (89): 174–175. April 1965. MTE:362. ISSN 0025-5718. https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf. Retrieved 2016-03-13. 
  8. ↑ "Table Errata 365: Milton Abramowitz & Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964.". Mathematics of Computation 19 (90): 360–363. April 1965. MTE:365. ISSN 0025-5718. https://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf. Retrieved 2016-03-13. 
  9. ↑ "Errata 373: Milton Abramowitz & Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., first printing, June 1964.". Mathematics of Computation 19 (91): 527–528. July 1965. doi:10.2307/2003725. MTE:373. ISSN 0025-5718. https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf. Retrieved 2016-03-13. 
  10. ↑ "Errata 376: Milton Abramowitz & Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964.". Mathematics of Computation 19 (92): 705–706. October 1965. doi:10.2307/2003991. MTE:376. ISSN 0025-5718. https://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf. Retrieved 2016-03-13. 
  11. ↑ 11.0 11.1 11.2 11.3 "Errata 379: Milton Abramowitz & Irene A. Stegun, Editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964, and all known reprints.". Mathematics of Computation 20 (93): 202–206. January 1966. MTE:379. ISSN 0025-5718. https://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf. Retrieved 2016-03-13. 
  12. ↑ "Errata 388: Milton Abramowitz & Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., first printing, June 1964.". Mathematics of Computation 20 (94): 344. April 1966. MTE:388. ISSN 0025-5718. https://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf. Retrieved 2016-03-13. 
  13. ↑ 13.0 13.1 13.2 "Errata 393: Milton Abramowitz & Irene A. Stegun, Editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964.". Mathematics of Computation 20 (95): 469–471. July 1966. doi:10.2307/2003630. MTE:393. ISSN 0025-5718. https://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf. Retrieved 2016-03-13. 
  14. ↑ 14.0 14.1 Danos, Michael; Rafelski, Johann; Abramowitz, Milton et al., eds (1984). Pocketbook of Mathematical Functions. Thun, Frankfurt/Main: Verlag Harri Deutsch. ISBN 978-3-87144-818-8. https://books.google.com/books?id=rAMbAQAAIAAJ. Retrieved 2016-03-13.  (468 pages)
  15. ↑ 15.0 15.1 15.2 15.3 15.4 "Reviews and Descriptions of Tables and Books 18: Milton Abramowitz and Irene A. Stegun. Pocketbook of Mathematical Functions - Abridged Edition of Handbook of Mathematical Functions. Material selected by Michael Danos and Johann Rafelski". Mathematics of Computation 50 (182): 646–647. April 1988. doi:10.2307/2008636. MSC:33-00,65A05. ISSN 0025-5718. https://www.ams.org/journals/mcom/1988-50-182/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf. Retrieved 2016-03-13. 
  16. ↑ Abramowitz, Milton; Stegun, Irene Ann, eds (1983). "Chapter 25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. pp. 886. LCCN 65-12253. ISBN 978-0-486-61272-0. http://www.math.sfu.ca/~cbm/aands/page_886.htm. 
  17. ↑ "Boole's Rule - from Wolfram MathWorld". Mathworld.wolfram.com. 2009-10-27. http://mathworld.wolfram.com/BoolesRule.html. 

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Further reading

  • Abramowitz, Milton; Stegun, Irene Ann, eds (1983). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. LCCN 65-12253. ISBN 978-0-486-61272-0. 
  • Lide, David R., ed (January 2001). "Handbook of Mathematical Functions". A Century of Excellence in Measurements Standards and Technology - A Chronicle of Selected NBS/NIST Publications 1901–2000. Washington, D.C., USA: U.S. Department of Commerce, National Institute of Standards and Technology (NIST) / CRC Press. pp. 135–139. CODEN NSPUE2. NIST Special Publication 958. 20402–9325. ISBN 978-0-8493-1247-2. http://nvl.nist.gov/pub/nistpubs/sp958-lide/135-139.pdf. Retrieved 2016-03-13.  (NB. A history of the activities leading up to and surrounding the development of the Handbook.)

External links



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