Abramowitz and Stegun: Difference between revisions

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==Overview==
Since it was first published in 1964, the 1046 page ''Handbook'' has been one of the most comprehensive sources of information on [[special function]]s, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of [[applied mathematics]].<ref name="REV_89_1">{{cite journal |title=Reviews and Descriptions of Tables and Books 1: Milton Abramowitz & Irene A. Stegun (editors). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1964 |author-first=John William |author-last=Wrench, Jr. |author-link=John William Wrench, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=19 |number=89 |date=April 1965 |pages=147–149 |doi=10.2307/2004114 |jstor=2004114 |id=MSC:A-F,H-M,R,SX |url=http://www.ams.org/journals/mcom/1965-19-0891090/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf |access-date=2016-03-13}}</ref><ref name="Boisvert_2011">{{cite journal |author-first1=Boisvert |author-last1=Ronald F. |author-first2=Charles W. |author-last2=Clark |author-first3=Daniel W. |author-last3=Lozier |author-first4=Frank William John |author-last4=Olver |author-link4=Frank Olver |title=A Special Functions Handbook for the Digital Age |journal=[[Notices of the American Mathematical Society]] (NAMS) |volume=58 |issue=7 |date=2011 |pages=905–911 |url=http://www.ams.org/notices/201107/rtx110700905p.pdf |access-date=2016-03-13}}</ref> 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 system]]s have replaced the [[mathematical table|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".{{fact}}
 
{{Quotation|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<ref name="Berry_1997">{{cite journal |author-first=Michael |author-last=Berry |author-link=Michael Berry (physicist) |title=Christmas books: ... Or maybe two or three ... |journal=[[New Scientist]] |date=1997-11-22 |url=https://www.newscientist.com/article/mg15621095.500-christmas-books-----or-maybe-two-or-three---.html |access-date=2016-03-13}} [http://michaelberryphysics.files.wordpress.com/2013/07/berry288.pdf]</ref> said he would take the Handbook.
Original NBS edition:
 
*1st printing: June 1964; [[errata]]:<ref name="MTE_362">{{cite journal |doi=10.1090/S0025-5718-65-99955-2 }}</ref><ref name="MTE_365">{{cite journal |doi=10.1090/S0025-5718-65-99949-7 }}</ref><ref name="MTE_373">{{cite journal |doi=10.1090/S0025-5718-65-99243-4 }}</ref><ref name="MTE_376">{{cite journal |doi=10.1090/S0025-5718-65-99941-2 }}</ref><ref name="MTE_379">{{cite journal |doi=10.1090/S0025-5718-66-99937-6 }}</ref><ref name="MTE_388">{{cite journal |doi=10.1090/S0025-5718-66-99637-2 }}</ref><ref name="MTE_393">{{cite journal |doi=10.1090/S0025-5718-66-99916-9 }}</ref>
*1st printing: June 1964; [[errata]]:<ref name="MTE_362">{{cite journal |title=Table Errata 362: 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 |author-first1=J. D. |author-last1=Cloud |author-first2=H. H. |author-last2=Denman |author-first3=John William |author-last3=Wrench, Jr. |author-link3=John William Wrench, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=19 |number=89 |date=April 1965 |pages=174–175 |jstor=2004148 |id=MTE:362 |url=http://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf |access-date=2016-03-13}}</ref><ref name="MTE_365">{{cite journal |title=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 |author-first1=Irene Ann |author-last1=Stegun |author-link1=Irene A. Stegun |author-first2=H. R. |author-last2=Aggarwal |author-first3=C. M. |author-last3=Ablow |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=19 |number=90 |date=April 1965 |pages=360–363 |jstor=2003399 |id=MTE:365 |url=http://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf |access-date=2016-03-13}}</ref><ref name="MTE_373">{{cite journal |title=Errata 373: 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 |author-first=Henry C. |author-last=Thacher, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=19 |number=91 |date=July 1965 |pages=527–528 |jstor=2003725 |doi=10.2307/2003725 |id=MTE:373 |url=http://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf |access-date=2016-03-13}}</ref><ref name="MTE_376">{{cite journal |title=Errata 376: 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 |author-first1=Irwin |author-last1=Manning |author-first2=J. G. C. |author-last2=Templeton |author-first3=Henry C. |author-last3=Thacher, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=19 |number=92 |date=October 1965 |pages=705–706 |jstor=2003991 |doi=10.2307/2003991 |id=MTE:376 |url=http://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf |access-date=2016-03-13}}</ref><ref name="MTE_379">{{cite journal |title=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 |author-first1=Daniel |author-last1=Shanks |author-link1=Daniel Shanks |author-first2=Michael |author-last2=Greenebaum |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=20 |number=93 |date=January 1966 |pages=202–206 |jstor=2004328 |id=MTE:379 |url=http://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf |access-date=2016-03-13}}</ref><ref name="MTE_388">{{cite journal |title=Errata 388: 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 |author-first1=Van E. |author-last1=Wood |author-first2=René |author-last2=Gamper |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=20 |number=94 |date=April 1966 |page=344 |jstor=2003533 |id=MTE:388 |url=http://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf |access-date=2016-03-13}}</ref><ref name="MTE_393">{{cite journal |title=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 |author-first1=Herbert E. |author-last1=Salzer |author-first2=Robert S. |author-last2=Johnson |author-first3=Henry E. |author-last3=Fettis |author-first4=James C. |author-last4=Caslin |author-first5=Paul |author-last5=Concus |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=20 |number=95 |date=July 1966 |pages=469–471 |jstor=2003630 |doi=10.2307/2003630 |id=MTE:393 |url=http://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf |access-date=2016-03-13}}</ref>
*2nd printing with corrections: November 1964; errata:<ref name="MTE_379"/>
*3rd printing with corrections: March 1965; errata:<ref name="MTE_379"/><ref name="MTE_393"/>
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:<ref name="MTE_373"/><ref name="MTE_393"/><!-- pages 256, 329. --><ref name="MTE_444">{{cite journal |doi=10.1090/S0025-5718-69-99640-9 }}</ref><ref name="MTE_638">{{cite journal |doi=10.1090/S0025-5718-97-00823-5 }}</ref>
Unresolved errata:<ref name="MTE_373"/><ref name="MTE_393"/><!-- pages 256, 329. --><ref name="MTE_444">{{cite journal |title=Table Errata 444: 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 |author-first=Henry E. |author-last=Fettis |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=23 |number=108 |date=October 1969 |page=891<!-- 891-892+s15-s17 --> |jstor=2004993 |id=MTE:444 |url=http://www.ams.org/journals/mcom/1969-23-108/S0025-5718-69-99640-9/S0025-5718-69-99640-9.pdf |access-date=2016-03-13}}</ref><ref name="MTE_638">{{cite journal |author-first=James Harold |author-last=Davenport |author-link=James Harold Davenport |title=Table Errata 638: Abramowitz, M., & Stegun, I. Handbook of mathematical functions with formulas, graphs, and mathematical tables |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=71 |number=240 |date=October 2002 |page=1801 |jstor=4099976 |id=MTE:638. PII:S0025-5718-97-00823-5. CODEN:MCMPAF}}</ref>
 
=={{anchor|Pocketbook|DLMF}}Related projects==
[[Michael Danos]] and [[Johann Rafelski]] edited the “''Pocketbook of Mathematical Functions''”, published by [[Verlag Harri Deutsch]] in 1984.<ref name="Danos_1984">{{cite book |title=Pocketbook of Mathematical Functions |editor-first1=Michael |editor-last1=Danos |editor-first2=Johann |editor-last2=Rafelski |editor-link2=Johann Rafelski |editor-first3=Milton |editor-last3=Abramowitz |editor-link3=Milton Abramowitz |editor-first4=Irene Ann |editor-last4=Stegun |editor-link4=Irene Ann Stegun |publisher=[[Verlag Harri Deutsch]] |location=Thun, Frankfurt/Main |date=1984 |isbn=3-87144-818-4 |id={{ISBN|978-3-87144-818-8}} |url=https://books.google.com/books/about/Pocketbook_of_Mathematical_Functions.html?id=rAMbAQAAIAAJ |access-date=2016-03-13}} (468 pages)</ref><ref name="REV_182_18">{{cite journal |title=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 |author-first=John William |author-last=Wrench, Jr. |author-link=John William Wrench, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |publisher=[[American Mathematical Society]] |volume=50 |number=182 |date=April 1988 |pages=646–647 |jstor=2008636 |doi=10.2307/2008636 |id=MSC:33-00,65A05 |url=http://www.ams.org/journals/mcom/1988-50-1821090/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf |access-date=2016-03-13}}</ref> 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,<ref name="Danos_1984"/> which, by this time, could be easily calculated with [[scientific pocket calculator]]s.<ref name="REV_182_18"/> The references were removed as well.<ref name="REV_182_18"/> Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter.<ref name="REV_182_18"/> The numbering of formulas was kept for easier cross-reference.<ref name="REV_182_18"/>
 
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]].<ref name="NIST_2010">{{cite book |title=NIST Handbook of Mathematical Functions |title-link=NIST Handbook of Mathematical Functions |editor1-first=Frank William John |editor1-last=Olver |editor1-link=Frank William John Olver |editor2-first=Daniel W. |editor2-last=Lozier |editor3-first=Ronald F. |editor3-last=Boisvert |editor4-first=Charles W. |editor4-last=Clark |year=2010 |publisher=[[National Institute of Standards and Technology]] (NIST), [[U.S. Department of Commerce]], [[Cambridge University Press]] |isbn=978-0-521-19225-5 |mr=2723248}} [http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521140638]</ref>