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Abramowitz and Stegun (AS) is the informal name of a 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 May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.[1]

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
Page 97 showing part of a table of common logarithms
Author Milton Abramowitz and Irene Stegun
Country United States
Language English
Genre Math
Publisher United States Department of Commerce, National Bureau of Standards (NBS)
Publication date
ISBN 0-486-61272-4
OCLC 18003605



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] 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[4] 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[5]


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:[6][7][8][9][10][11][12]
  • 2nd printing with corrections: November 1964; errata:[10]
  • 3rd printing with corrections: March 1965; errata:[10][12]
  • 4th printing with corrections: December 1965; errata:[10][12]
  • 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

Reprint edition by Dover Publications:

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


Up to the tenth printing of the original NBS edition in December 1972, corrections were incorporated on pages 2–3,[6] 6–8,[7] 10, 15,[7] 19–20, 25,[7] 76, 85,[9] 91, 102, 187, 189–197, 218, 223, 225, 233, 250,[7] 255,[7] 260–263,[6][7][11] 268, 271–273, 292,[7] 302,[12] 328,[7] 332,[7] 333–337,[7] 362,[7] 365,[7] 415,[12] 423, 438–440,[6] 443,[6] 445, 447, 449, 451, 484,[7] 498, 505–506, 509–510,[7] 543, 556, 558, 562,[12] 571, 595, 599, 600, 722–723, 739, 742, 744, 746,[7] 752,[7] 756, 760–765, 774,[7] 777–785,[7] 790, 797,[7] 801, 822–823,[7] 832, 835, 844,[7] 886–889,[10][11] 897, 914,[9] 915, 920, 930–931, 936, 940–941, 944–950,[7][9] 953, 960, 963, 989–990, 1010 and 1026.[10]

The ninth reprint edition by Dover Publications incorporates additional corrections on pages 18, 79, 80, 82, 408, 450, 786, 825 and 934.

As a side-note, the Dover paperback edition (SBN 468-61272-4) cover names the second editor "Irene A. Segun" instead of Stegun. This error is sometimes used to illustrate the human trait of looking in every place except the most obvious one.

Unresolved errata:[8][12][13][14]

Related projectsEdit

Michael Danos and Johann Rafelski edited the “Pocketbook of Mathematical Functions”, published by Verlag Harri Deutsch in 1984.[15][16] 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,[15] which, by this time, could be easily calculated with scientific pocket calculators.[16] The references were removed as well.[16] Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter.[16] The numbering of formulas was kept for easier cross-reference.[16]

A digital successor to the Handbook, long under development at NIST, was released as the “Digital Library of Mathematical Functions” (DLMF) on May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.[1]

See alsoEdit


  1. ^ a b Olver, Frank William John; Lozier, Daniel W.; Boisvert, Ronald F.; Clark, Charles W., eds. (2010). NIST Handbook of Mathematical Functions. National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Cambridge University Press. ISBN 978-0-521-19225-5. MR 2723248.  [1]
  2. ^ "Reviews and Descriptions of Tables and Books". Mathematics of Computation. 19 (89): 147–9. 1965. doi:10.1090/S0025-5718-65-99956-4. 
  3. ^ Ronald F., Boisvert; Clark, Charles W.; Lozier, Daniel W.; Olver, Frank William John (2011). "A Special Functions Handbook for the Digital Age" (PDF). Notices of the American Mathematical Society. 58 (7): 905–911. Retrieved 2016-03-13. 
  4. ^ Berry, Michael (1997-11-22). "Christmas books: ... Or maybe two or three ..." New Scientist. Retrieved 2016-03-13.  [2]
  5. ^ "NIST at 100: Foundations for Progress, 1964: Mathematics Handbook Becomes Best Seller". 2001. Archived from the original on 2016-03-13. Retrieved 2016-03-13. 
  6. ^ a b c d e "Table Errata". Mathematics of Computation. 19 (89): 174. 1965. doi:10.1090/S0025-5718-65-99955-2. 
  7. ^ a b c d e f g h i j k l m n o p q r s t u v w "Table Errata". Mathematics of Computation. 19 (90): 360–3. 1965. doi:10.1090/S0025-5718-65-99949-7. 
  8. ^ a b "Errata". Mathematics of Computation. 19 (91): 527–8. 1965. doi:10.1090/S0025-5718-65-99243-4. 
  9. ^ a b c d "Errata". Mathematics of Computation. 19 (92): 705–6. 1965. doi:10.1090/S0025-5718-65-99941-2. 
  10. ^ a b c d e f "Table Errata". Mathematics of Computation. 20 (93): 202–6. 1966. doi:10.1090/S0025-5718-66-99937-6. 
  11. ^ a b c "Table Errata". Mathematics of Computation. 20 (94): 344. 1966. doi:10.1090/S0025-5718-66-99637-2. 
  12. ^ a b c d e f g "Errata". Mathematics of Computation. 20 (95): 468–71. 1966. doi:10.1090/S0025-5718-66-99916-9. 
  13. ^ "Table Errata". Mathematics of Computation. 23 (108): 891–2. 1969. doi:10.1090/S0025-5718-69-99640-9. 
  14. ^ Tourigny, Y; Baines, M. J (1997). "Analysis of an algorithm for generating locally optimal meshes for L2 approximation by discontinuous piecewise polynomials". Mathematics of Computation. 66 (218): 623–50. doi:10.1090/S0025-5718-97-00823-5. 
  15. ^ a b Danos, Michael; Rafelski, Johann; Abramowitz, Milton; Stegun, Irene Ann, eds. (1984). Pocketbook of Mathematical Functions. Thun, Frankfurt/Main: Verlag Harri Deutsch. ISBN 3-87144-818-4. ISBN 978-3-87144-818-8. Retrieved 2016-03-13.  (468 pages)
  16. ^ a b c d e "Reviews and Descriptions of Tables and Books". Mathematics of Computation. 50 (182): 639–51. 1988. doi:10.1090/S0025-5718-88-99805-5. 
  17. ^ "Boole's Rule - from Wolfram MathWorld". 2009-10-27. Retrieved 2009-11-13. 
  18. ^ Zucker, Ruth (1983) [June 1964]. "Chapter 25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis". In Abramowitz, Milton; Stegun, Irene Ann. 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. p. 886. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253. 

Further readingEdit

External linksEdit