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{{short description|1964 mathematical reference work edited by M. Abramowitz and I. Stegun}}
{{short description|1964 mathematical reference work edited by M. Abramowitz and I. Stegun}}
{{use dmy dates|date=December 2021|cs1-dates=y}}
{{use list-defined references|date=December 2021}}
{{Infobox book | <!-- See Wikipedia:WikiProject_Novels or Wikipedia:WikiProject_Books -->
{{Infobox book | <!-- See Wikipedia:WikiProject_Novels or Wikipedia:WikiProject_Books -->
| name = Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
| name = Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
| image = Abramowitz&Stegun.page97.agr.jpg
| image = Handbook of Mathematical Functions, by Abramowitz and Stegun, cover.jpg
| caption = Page 97 showing part of a table of [[common logarithm]]s
| caption = Cover of the ninth printing, 1970
| author = [[Milton Abramowitz]] and [[Irene Stegun]]
| author = [[Milton Abramowitz]] and [[Irene Stegun]]
| country = United States
| country = United States
Line 14: Line 16:
}}
}}


'''''Abramowitz and Stegun''''' ('''''AS''''') is the informal name of a 1964 [[mathematics|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]].<ref name="NIST_2010"/>
'''''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]].<ref name="NIST_2010"/>


==Overview==
==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"/><ref name="Boisvert_2011"/> The notation used in the ''Handbook'' is the ''[[de facto]]'' standard for much of applied mathematics today.
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="Miller_1968"/><ref name="REV_89_1"/><ref name="Boisvert_2011"/> 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".
At the time of its publication, the ''Handbook'' was an essential resource for practitioners. Nowadays, [[scientific calculator]]s, [[numerical analysis]] software packages, and [[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".


{{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"/> said he would take the Handbook.
{{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"/> 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]]<ref name="NIST_2001"/>}}
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]]<ref name="NIST_2001"/>}}

[[file:Abramowitz&Stegun.page97.agr.jpg|right|thumb|Page 97 showing part of a table of [[common logarithm]]s]]


The chapters are:
The chapters are:
# Mathematical Constants
# Mathematical Constants
# Physical Constants and Conversion Factors
# Physical Constants and Conversion Factors
# Elementary Analytical Methods
# Elementary [[analysis (mathematics)|Analytical]] Methods
# Elementary Transcendental Functions
# Elementary [[Transcendental function|Transcendental Functions]]
# Exponential Integral and Related Functions
# [[Exponential integral|Exponential Integral]] and Related Functions
# Gamma Function and Related Functions
# [[Gamma function|Gamma Function]] and Related Functions
# Error Function and Fresnel Integrals
# [[Error Function]] and [[Fresnel integral|Fresnel Integrals]]
# Legendre Functions
# [[Legendre function|Legendre Functions]]
# Bessel Functions of Integral Order
# [[Bessel function|Bessel Functions]] of Integral Order
# Bessel Functions of Fractional Order
# Bessel Functions of Fractional Order
# Integrals of Bessel Functions
# Integrals of Bessel Functions
# Struve Functions and Related Functions
# [[Struve function|Struve Functions]] and Related Functions
# Confluent Hypergeometric Functions
# [[Confluent hypergeometric function|Confluent Hypergeometric Function]]s
# Coulomb Wave Functions
# [[Coulomb wave function|Coulomb Wave Functions]]
# Hypergeometric Functions
# [[Hypergeometric functions|Hypergeometric Functions]]
# Jacobian Elliptic Functions and Theta Functions
# [[Jacobian elliptic function|Jacobian Elliptic Functions]] and [[Theta function|Theta Functions]]
# Elliptic Integrals
# [[Elliptic integral|Elliptic Integrals]]
# Weierstrass Elliptic and Related Functions
# [[Weierstrass elliptic function|Weierstrass Elliptic]] and Related Functions
# Parabolic Cylinder Functions
# [[parabolic cylinder function|Parabolic Cylinder Functions]]
# Mathieu Functions
# [[Mathieu functions|Mathieu Functions]]
# Spheroidal Wave Functions
# [[Spheroidal wave function|Spheroidal Wave Functions]]
# Orthogonal Polynomials
# [[Orthogonal polynomial|Orthogonal Polynomials]]
# Bernoulli and Euler Polynomials, Riemann Zeta Function
# [[Bernoulli polynomials|Bernoulli and Euler Polynomials]], [[Riemann Zeta function|Riemann Zeta Function]]
# Combinatorial Analysis
# [[Combinatorial analysis|Combinatorial Analysis]]
# Numerical Interpolation, Differentiation, and Integration
# Numerical Interpolation, Differentiation, and Integration
# Probability Functions
# [[Probability]] Functions
# Miscellaneous Functions
# Miscellaneous Functions
# Scales of Notation
# Scales of Notation
# Laplace Transforms
# [[Laplace Transform]]s


==Editions==
==Editions==
Line 75: Line 79:
Reprint edition by [[Dover Publications]]:
Reprint edition by [[Dover Publications]]:


* 1st printing: 1965
* 1st printing<!-- (1046 pages, paperback, USD 4.50) -->: 1965<ref name="Miller_1968"/>
* ?
* ?
* 9th printing with additional corrections (based on 10th printing of NBS edition with corrections)<ref group="nb" name="NB_Errata"/>
* 9th printing with additional corrections (based on 10th printing of NBS edition with corrections)<ref group="nb" name="NB_Errata"/>
Line 82: Line 86:
[[Michael Danos]] and [[Johann Rafelski]] edited the ''Pocketbook of Mathematical Functions'', published by [[Verlag Harri Deutsch]] in 1984.<ref name="Danos_1984"/><ref name="REV_182_18"/> 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"/>
[[Michael Danos]] and [[Johann Rafelski]] edited the ''Pocketbook of Mathematical Functions'', published by [[Verlag Harri Deutsch]] in 1984.<ref name="Danos_1984"/><ref name="REV_182_18"/> 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"/>
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]].<ref name="NIST_2010"/>


==See also==
==See also==
* [[Mathematical Tables Project]], a 1938–1948 [[Works Progress Administration]] (WPA) project to calculate mathematical tables, including those later used in Abramowitz and Stegun's Handbook of Mathematical Functions
* [[Mathematical Tables Project]], a 1938–1948 [[Works Progress Administration]] (WPA) project to calculate mathematical tables, including those later used in Abramowitz and Stegun's Handbook of Mathematical Functions
* [[Numerical analysis]]
* [[Numerical analysis]]
* [[Rubber Book|Rubber book]], a ''Handbook of Chemistry & Physics''
* [[Reference work|Reference book]]
* [[Handbook]]
* ''[[MAOL table book|MAOL]]'', a Finnish handbook for science
* ''[[BINAS]]'', a Dutch science handbook
* [[Philip J. Davis]], author of the [[Gamma function]] section and other sections of the book
* [[Philip J. Davis]], author of the [[Gamma function]] section and other sections of the book
* [[Louis Melville Milne-Thomson]], author of the book chapters on [[elliptic integral|elliptic integrals]] and [[Jacobi elliptic functions]]
* [[Louis Melville Milne-Thomson]], author of the book chapters on [[elliptic integral|elliptic integrals]] and [[Jacobi elliptic functions]]
* [[Digital Library of Mathematical Functions]] (DLMF), from the [[National Institute of Standards and Technology]] (NIST), is intended to be a replacement for Abramowitz and Stegun's Handbook of Mathematical Functions
* [[Digital Library of Mathematical Functions]] (DLMF), from the [[National Institute of Standards and Technology]] (NIST), is intended to be a replacement for Abramowitz and Stegun's Handbook of Mathematical Functions
* [[Boole's rule]], a mathematical rule of integration sometimes known as Bode's rule, due to a typo in Abramowitz and Stegun (1972, p.&nbsp;886)<ref name="Abramowitz_1972"/><ref group="nb" name="NB_Errata"/> that was subsequently propagated.<ref name="Wolfram_2009"/>
* [[Boole's rule]], a mathematical rule of integration sometimes known as Bode's rule, due to a typo in Abramowitz and Stegun (1972, p.&nbsp;886)<ref name="Abramowitz_1972"/><ref group="nb" name="NB_Errata"/> that was subsequently propagated.<ref name="Wolfram_2009"/>
* [[On-Line Encyclopedia of Integer Sequences]]


==Notes==
==Notes==
{{reflist|group="nb"|refs=
{{reflist|group="nb"|refs=
{{r|group="nb"|name="NB_Errata"|r=Up to the tenth printing of the original NBS edition in December 1972, corrections were incorporated on pages 2–3,<ref name="MTE_362"/> 6–8,<ref name="MTE_365"/> 10, 15,<ref name="MTE_365"/> 19–20, 25,<ref name="MTE_365"/> 76, 85,<ref name="MTE_376"/> 91, 102, 187, 189–197, 218, 223, 225, 233, 250,<ref name="MTE_365"/> 255,<ref name="MTE_365"/> 260–263,<ref name="MTE_362"/><ref name="MTE_365"/><ref name="MTE_388"/> 268, 271–273, 292,<ref name="MTE_365"/> 302,<ref name="MTE_393"/> 328,<ref name="MTE_365"/> 332,<ref name="MTE_365"/> 333–337,<ref name="MTE_365"/> 362,<ref name="MTE_365"/> 365,<ref name="MTE_365"/> 415,<ref name="MTE_393"/> 423, 438–440,<ref name="MTE_362"/> 443,<ref name="MTE_362"/> 445, 447, 449, 451, 484,<ref name="MTE_365"/> 498, 505–506, 509–510,<ref name="MTE_365"/> 543, 556, 558, 562,<ref name="MTE_393"/> 571, 595, 599, 600, 722–723, 739, 742, 744, 746,<ref name="MTE_365"/> 752,<ref name="MTE_365"/> 756, 760–765, 774,<ref name="MTE_365"/> 777–785,<ref name="MTE_365"/> 790, 797,<ref name="MTE_365"/> 801, 822–823,<ref name="MTE_365"/> 832, 835, 844,<ref name="MTE_365"/> 886–889,<ref name="MTE_379"/><ref name="MTE_388"/> 897, 914,<ref name="MTE_376"/> 915, 920, 930–931, 936, 940–941, 944–950,<ref name="MTE_365"/><ref name="MTE_376"/> 953, 960, 963, 989–990, 1010 and 1026.<ref name="MTE_379"/> The [[Dover Publications]] paperback edition ({{SBN|468-61272-4|invalid1=yes}}) cover names the second editor as "Irene A. Segun" instead of Stegun. The ninth reprint edition by Dover incorporates additional corrections on pages 18, 79, 80, 82, 408, 450, 786, 825 and 934. Unresolved errata include:<ref name="MTE_373"/><ref name="MTE_393"/><!-- pages 256, 329. --><ref name="MTE_444"/><ref name="MTE_638"/>}}
{{r|group="nb"|name="NB_Errata"|r=Up to the tenth printing of the original NBS edition in December 1972, corrections were incorporated on pages 2–3,<ref name="MTE_362"/> 6–8,<ref name="MTE_365"/> 10, 15,<ref name="MTE_365"/> 19–20, 25,<ref name="MTE_365"/> 76, 85,<ref name="MTE_376"/> 91, 102, 187, 189–197, 218, 223, 225, 233, 250,<ref name="MTE_365"/> 255,<ref name="MTE_365"/> 260–263,<ref name="MTE_362"/><ref name="MTE_365"/><ref name="MTE_388"/> 268, 271–273, 292,<ref name="MTE_365"/> 302,<ref name="MTE_393"/> 328,<ref name="MTE_365"/> 332,<ref name="MTE_365"/> 333–337,<ref name="MTE_365"/> 362,<ref name="MTE_365"/> 365,<ref name="MTE_365"/> 415,<ref name="MTE_393"/> 423, 438–440,<ref name="MTE_362"/> 443,<ref name="MTE_362"/> 445, 447, 449, 451, 484,<ref name="MTE_365"/> 498, 505–506, 509–510,<ref name="MTE_365"/> 543, 556, 558, 562,<ref name="MTE_393"/> 571, 595, 599, 600, 722–723, 739, 742, 744, 746,<ref name="MTE_365"/> 752,<ref name="MTE_365"/> 756, 760–765, 774,<ref name="MTE_365"/> 777–785,<ref name="MTE_365"/> 790, 797,<ref name="MTE_365"/> 801, 822–823,<ref name="MTE_365"/> 832, 835, 844,<ref name="MTE_365"/> 886–889,<ref name="MTE_379"/><ref name="MTE_388"/> 897, 914,<ref name="MTE_376"/> 915, 920, 930–931, 936, 940–941, 944–950,<ref name="MTE_365"/><ref name="MTE_376"/> 953, 960, 963, 989–990, 1010 and 1026.<ref name="MTE_379"/> The [[Dover Publications]] paperback edition ({{SBN|486612724}}) cover names the second editor as "Irene A. Segun" instead of Stegun. The ninth reprint edition by Dover incorporates additional corrections on pages 18, 79, 80, 82, 408, 450, 786, 825 and 934. Unresolved errata include:<ref name="MTE_373"/><ref name="MTE_393"/><!-- pages 256, 329. --><ref name="MTE_444"/><ref name="MTE_638"/>}}
}}
}}


==References==
==References==
{{reflist|refs=
{{reflist|refs=
<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 |date=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>
<ref name="NIST_2010">{{cite book |title=NIST Handbook of Mathematical Functions |title-link=NIST Handbook of Mathematical Functions |editor-first1=Frank William John |editor-last1=Olver |editor-link1=Frank William John Olver |editor-first2=Daniel W. |editor-last2=Lozier |editor-first3=Ronald F. |editor-last3=Boisvert |editor-first4=Charles W. |editor-last4=Clark |date=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>
<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 |volume=19 |number=89 |date=April 1965 |doi=10.2307/2004114 |jstor=2004114 |id=MSC:A-F,H-M,R,SX |pages=147–149 |url=https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909152953/https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf |archive-date=2021-09-09}}</ref>
<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, Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964, xiv + 1046p., 27 cm. Price $6.50. |author-first=John William |author-last=Wrench, Jr. |author-link=John William Wrench, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=19 |number=89 |date=April 1965 |doi=10.2307/2004114 |jstor=2004114 |id=MSC:A-F,H-M,R,SX |pages=147–149 |url=https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909152953/https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99956-4/S0025-5718-65-99956-4.pdf |archive-date=2021-09-09}}</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=https://www.ams.org/notices/201107/rtx110700905p.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144026/https://www.ams.org/notices/201107/rtx110700905p.pdf |archive-date=2021-09-09}}</ref>
<ref name="Boisvert_2011">{{cite journal |author-first1=Ronald F. |author-last1=Boisvert |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=https://www.ams.org/notices/201107/rtx110700905p.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144026/https://www.ams.org/notices/201107/rtx110700905p.pdf |archive-date=2021-09-09}}</ref>
<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 |url-status= |archive-url= |archive-date=}} [https://web.archive.org/web/20210909151100/https://michaelberryphysics.files.wordpress.com/2013/07/berry288.pdf<!-- http://michaelberryphysics.files.wordpress.com/2013/07/berry288.pdf -->]</ref>
<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 |url-status= |archive-url= |archive-date=}} [https://web.archive.org/web/20210909151100/https://michaelberryphysics.files.wordpress.com/2013/07/berry288.pdf<!-- http://michaelberryphysics.files.wordpress.com/2013/07/berry288.pdf -->]</ref>
<ref name="NIST_2001">{{cite web |title=NIST at 100: Foundations for Progress, 1964: Mathematics Handbook Becomes Best Seller |date=2001 |url=https://www.nist.gov/centennial/ph_spaceage.cfm#1964 |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20160313160527/https://www.nist.gov/centennial/ph_spaceage.cfm#1964 |archive-date=2016-03-13}}</ref>
<ref name="NIST_2001">{{cite web |title=NIST at 100: Foundations for Progress, 1964: Mathematics Handbook Becomes Best Seller |work=NIST |date=2001 |url=https://www.nist.gov/centennial/ph_spaceage.cfm#1964 |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20160313160527/https://www.nist.gov/centennial/ph_spaceage.cfm#1964 |archive-date=2016-03-13}}</ref>
<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 |volume=19 |number=89 |date=April 1965 |jstor=2004148 |id=MTE:362 |pages=174–175 |url=https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144048/https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf |archive-date=2021-09-09}}</ref>
<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, No. 55, U. S. Government Printing Office, Washington, D. C., 1964. |author-first1=John D. |author-last1=Cloud<!-- Manhattan Beach, California --> |author-first2=Harry H. |author-last2=Denman<!-- Wayne State University, Detroit --> |author-first3=John William |author-last3=Wrench, Jr. |author-link3=John William Wrench, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=19 |number=89 |date=April 1965 |jstor=2004148 |id=MTE:362 |pages=174–175 |url=https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144048/https://www.ams.org/journals/mcom/1965-19-089/S0025-5718-65-99955-2/S0025-5718-65-99955-2.pdf |archive-date=2021-09-09}}</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 |volume=19 |number=90 |date=April 1965 |jstor=2003399 |id=MTE:365 |pages=360–363 |url=https://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144156/https://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf |archive-date=2021-09-09}}</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<!-- Stanford Research Institute, Menlo Park, California --> |author-first3=Clarence M. |author-last3=Ablow |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=19 |number=90 |date=April 1965 |jstor=2003399 |id=MTE:365 |pages=360–363 |url=https://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144156/https://www.ams.org/journals/mcom/1965-19-090/S0025-5718-65-99949-7/S0025-5718-65-99949-7.pdf |archive-date=2021-09-09}}</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 |volume=19 |number=91 |date=July 1965 |jstor=2003725 |doi=10.2307/2003725 |doi-access=free |id=MTE:373 |pages=527–528 |url=https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144012/https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf |archive-date=2021-09-09}}</ref>
<ref name="MTE_373">{{cite journal |title=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. |author-first=Henry C. |author-last=Thacher, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=19 |number=91 |date=July 1965 |jstor=2003725 |doi=10.2307/2003725 |doi-access=free |id=MTE:373 |pages=527–528 |url=https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144012/https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-65-99243-4/S0025-5718-65-99243-4.pdf |archive-date=2021-09-09}}</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 |volume=19 |number=92 |date=October 1965 |jstor=2003991 |doi=10.2307/2003991 |doi-access=free |id=MTE:376 |pages=705–706 |url=https://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909143945/https://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf |archive-date=2021-09-09}}</ref>
<ref name="MTE_376">{{cite journal |title=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. |author-first1=Irwin |author-last1=Manning |author-first2=James Gilbert Cooper |author-last2=Templeton<!-- :d:Q102162425--> |author-first3=Henry C. |author-last3=Thacher, Jr. |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=19 |number=92 |date=October 1965 |jstor=2003991 |doi=10.2307/2003991 |doi-access=free |id=MTE:376 |pages=705–706 |url=https://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909143945/https://www.ams.org/journals/mcom/1965-19-092/S0025-5718-65-99941-2/S0025-5718-65-99941-2.pdf |archive-date=2021-09-09}}</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 |volume=20 |number=93 |date=January 1966 |jstor=2004328 |id=MTE:379 |pages=202–206 |url=https://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144010/https://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf |archive-date=2021-09-09}}</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, and all known reprints. |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 |volume=20 |number=93 |date=January 1966 |jstor=2004328 |id=MTE:379 |pages=202–206 |url=https://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144010/https://www.ams.org/journals/mcom/1966-20-093/S0025-5718-66-99937-6/S0025-5718-66-99937-6.pdf |archive-date=2021-09-09}}</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 |volume=20 |number=94 |date=April 1966 |jstor=2003533 |id=MTE:388 |page=344 |url=https://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144020/https://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf |archive-date=2021-09-09}}</ref>
<ref name="MTE_388">{{cite journal |title=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. |author-first1=Van E. |author-last1=Wood |author-first2=René |author-last2=Gamper |journal=[[Mathematics of Computation]] |issn=0025-5718 |eissn=1088-6842 |volume=20 |number=94 |date=April 1966 |jstor=2003533 |id=MTE:388 |page=344 |url=https://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144020/https://www.ams.org/journals/mcom/1966-20-094/S0025-5718-66-99637-2/S0025-5718-66-99637-2.pdf |archive-date=2021-09-09}}</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 |volume=20 |number=95 |date=July 1966 |jstor=2003630 |doi=10.2307/2003630 |doi-access=free |id=MTE:393 |pages=469–471 |url=https://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144022/https://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf |archive-date=2021-09-09}}</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 |volume=20 |number=95 |date=July 1966 |jstor=2003630 |doi=10.2307/2003630 |doi-access=free |id=MTE:393 |pages=469–471 |url=https://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144022/https://www.ams.org/journals/mcom/1966-20-095/S0025-5718-66-99916-9/S0025-5718-66-99916-9.pdf |archive-date=2021-09-09}}</ref>
<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=978-3-87144-818-8 |url=https://books.google.com/books?id=rAMbAQAAIAAJ |access-date=2016-03-13 |url-status=live |archive-url= |archive-date=}} (468 pages)</ref>
<ref name="Danos_1984">{{cite book |title=Pocketbook of Mathematical Functions |editor1-first=Michael |editor1-last=Danos |editor2-first=Johann |editor2-last=Rafelski |editor-link2=Johann Rafelski |editor3-first=Milton |editor3-last=Abramowitz |editor-link3=Milton Abramowitz |editor4-first=Irene Ann |editor4-last=Stegun |editor-link4=Irene Ann Stegun |publisher=[[Verlag Harri Deutsch]] |location=Thun, Frankfurt/Main |date=1984 |isbn=978-3-87144-818-8 |url=https://books.google.com/books?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 |volume=50 |number=182 |date=April 1988 |jstor=2008636 |doi=10.2307/2008636 |id=MSC:33-00,65A05 |pages=646–647 |url=https://www.ams.org/journals/mcom/1988-50-182/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144028/https://www.ams.org/journals/mcom/1988-50-182/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf |archive-date=2021-09-09}}</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 |volume=50 |number=182 |date=April 1988 |jstor=2008636 |doi=10.2307/2008636 |id=MSC:33-00,65A05 |pages=646–647 |url=https://www.ams.org/journals/mcom/1988-50-182/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf |access-date=2016-03-13 |url-status=live |archive-url=https://web.archive.org/web/20210909144028/https://www.ams.org/journals/mcom/1988-50-182/S0025-5718-88-99805-5/S0025-5718-88-99805-5.pdf |archive-date=2021-09-09}}</ref>
<ref name="Wolfram_2009">{{cite web |title=Boole's Rule - from Wolfram MathWorld |publisher=Mathworld.wolfram.com |date=2009-10-27 |url=http://mathworld.wolfram.com/BoolesRule.html |access-date=2009-11-13 |url-status=live |archive-url=https://web.archive.org/web/20211201151621/https://mathworld.wolfram.com/BoolesRule.html |archive-date=2021-12-01}}</ref>
<ref name="Wolfram_2009">{{cite web |title=Boole's Rule - from Wolfram MathWorld |publisher=Mathworld.wolfram.com |date=2009-10-27 |url=http://mathworld.wolfram.com/BoolesRule.html |access-date=2009-11-13 |url-status=live |archive-url=https://web.archive.org/web/20211201151621/https://mathworld.wolfram.com/BoolesRule.html |archive-date=2021-12-01}}</ref>
<ref name="Abramowitz_1972">{{AS ref|25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis|886|author-first1=Ruth|author-last1=Zucker}}</ref>
<ref name="Abramowitz_1972">{{AS ref|25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis|886|author-first1=Ruth|author-last1=Zucker}}</ref>
<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 |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 |url-status=live |archive-url=https://web.archive.org/web/20190503031921/https://www.ams.org/journals/mcom/1969-23-108/S0025-5718-69-99640-9/S0025-5718-69-99640-9.pdf |archive-date=2019-05-03}}</ref>
<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 |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 |url-status=live |archive-url=https://web.archive.org/web/20190503031921/https://www.ams.org/journals/mcom/1969-23-108/S0025-5718-69-99640-9/S0025-5718-69-99640-9.pdf |archive-date=2019-05-03}}</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 |volume=71 |pages=1801 |number=240 |date=October 2002 |jstor=4099976 |id=MTE:638. PII:S0025-5718-97-00823-5. {{CODEN|MCMPAF}}}}</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 |volume=71 |pages=1801 |number=240 |date=October 2002 |jstor=4099976 |id=MTE:638. PII:S0025-5718-97-00823-5. {{CODEN|MCMPAF}}}}</ref>
<ref name="Miller_1968">{{cite magazine |title=Abramowitz, M., And I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications, Inc., 1965, 1046 pp., $4.50 (paperback) |department=Application Series |type=review |author-first=David Wendell |author-last=Miller<!-- Graduate School of Business, Columbia University, New York, [[:d:Q59630482]] --> |magazine=Management Science |issn= |date=February 1968 |volume=14 |issue=6 (#2) |jstor=2628175 |page=B-404 |url=https://ur.booksc.eu/book/59644937/4c5eeb |access-date=2021-12-31 |url-status= |archive-url= |archive-date= |quote=}}</ref>
}}
}}


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==External links==
==External links==
* A high quality scan of the book, in PDF and TIFF formats, hosted at [http://www.cs.bham.ac.uk/~aps/research/projects/as the University of Birmingham, UK]
* A high quality scan of the book, in PDF and TIFF formats, hosted at [http://www.cs.bham.ac.uk/~aps/research/projects/as the University of Birmingham, UK]
* The book in scanned format, hosted at [http://www.math.sfu.ca/~cbm/aands/ Simon Fraser University].
* The book in scanned format, now hosted at [https://personal.math.ubc.ca/~cbm/aands/ the University of British Columbia, CA] (formerly at Simon Fraser University). # but this scan dropped tables of numbers. For example, the pages contained table of abscissas and weights of Gauss quadrature formulas are omitted. Only formulas are scanned.
* [http://www.convertit.com/Go/ConvertIt/Reference/AMS55.asp Another scanned version] by ConvertIt.com
* [http://www.convertit.com/Go/ConvertIt/Reference/AMS55.asp Another scanned version] by ConvertIt.com
* [http://numerical.recipes/aands/ numerical.recipes ] download - NBS, Tenth Printing, December 1972, with Corrections - PDF without Search
* [http://numerical.recipes/aands/ numerical.recipes ] download - NBS, Tenth Printing, December 1972, with Corrections - PDF without Search
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[[Category:1964 non-fiction books]]
[[Category:1964 non-fiction books]]
[[Category:Handbooks and manuals]]
[[Category:Mathematics handbooks]]
[[Category:Mathematics books]]
[[Category:Mathematical tables]]
[[Category:Mathematical tables]]
[[Category:Numerical analysis]]
[[Category:Numerical analysis]]

Latest revision as of 03:52, 20 December 2024

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
Cover of the ninth printing, 1970
AuthorMilton Abramowitz and Irene Stegun
LanguageEnglish
GenreMath
PublisherUnited States Department of Commerce, National Bureau of Standards (NBS)
Publication date
1964
Publication placeUnited States
ISBN0-486-61272-4
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

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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, scientific calculators, numerical analysis software packages, and 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]
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

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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]
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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

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Notes

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  1. ^ a b c d e f g Up to the tenth printing of the original NBS edition in December 1972, corrections were incorporated on pages 2–3,[7] 6–8,[8] 10, 15,[8] 19–20, 25,[8] 76, 85,[10] 91, 102, 187, 189–197, 218, 223, 225, 233, 250,[8] 255,[8] 260–263,[7][8][12] 268, 271–273, 292,[8] 302,[13] 328,[8] 332,[8] 333–337,[8] 362,[8] 365,[8] 415,[13] 423, 438–440,[7] 443,[7] 445, 447, 449, 451, 484,[8] 498, 505–506, 509–510,[8] 543, 556, 558, 562,[13] 571, 595, 599, 600, 722–723, 739, 742, 744, 746,[8] 752,[8] 756, 760–765, 774,[8] 777–785,[8] 790, 797,[8] 801, 822–823,[8] 832, 835, 844,[8] 886–889,[11][12] 897, 914,[10] 915, 920, 930–931, 936, 940–941, 944–950,[8][10] 953, 960, 963, 989–990, 1010 and 1026.[11] The Dover Publications paperback edition (SBN 486612724) cover names the second editor as "Irene A. Segun" instead of Stegun. The ninth reprint edition by Dover incorporates additional corrections on pages 18, 79, 80, 82, 408, 450, 786, 825 and 934. Unresolved errata include:[9][13][18][19]

References

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  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. ^ a b Miller, David Wendell (February 1968). "Abramowitz, M., And I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications, Inc., 1965, 1046 pp., $4.50 (paperback)". Application Series. Management Science (review). Vol. 14, no. 6 (#2). p. B-404. JSTOR 2628175. Retrieved 2021-12-31.
  3. ^ Wrench, Jr., John William (April 1965). "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" (PDF). Mathematics of Computation. 19 (89): 147–149. doi:10.2307/2004114. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2004114. MSC:A-F,H-M,R,SX. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  4. ^ Boisvert, Ronald F.; 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 (NAMS). 58 (7): 905–911. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  5. ^ Berry, Michael (1997-11-22). "Christmas books: ... Or maybe two or three ..." New Scientist. Retrieved 2016-03-13. [2]
  6. ^ "NIST at 100: Foundations for Progress, 1964: Mathematics Handbook Becomes Best Seller". NIST. 2001. Archived from the original on 2016-03-13. Retrieved 2016-03-13.
  7. ^ a b c d e Cloud, John D.; Denman, Harry H.; Wrench, Jr., John William (April 1965). "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" (PDF). Mathematics of Computation. 19 (89): 174–175. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2004148. MTE:362. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  8. ^ a b c d e f g h i j k l m n o p q r s t u v w Stegun, Irene Ann; Aggarwal, H. R.; Ablow, Clarence M. (April 1965). "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" (PDF). Mathematics of Computation. 19 (90): 360–363. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2003399. MTE:365. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  9. ^ a b Thacher, Jr., Henry C. (July 1965). "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" (PDF). Mathematics of Computation. 19 (91): 527–528. doi:10.2307/2003725. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2003725. MTE:373. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  10. ^ a b c d Manning, Irwin; Templeton, James Gilbert Cooper; Thacher, Jr., Henry C. (October 1965). "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" (PDF). Mathematics of Computation. 19 (92): 705–706. doi:10.2307/2003991. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2003991. MTE:376. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  11. ^ a b c d e f Shanks, Daniel; Greenebaum, Michael (January 1966). "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" (PDF). Mathematics of Computation. 20 (93): 202–206. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2004328. MTE:379. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  12. ^ a b c Wood, Van E.; Gamper, René (April 1966). "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" (PDF). Mathematics of Computation. 20 (94): 344. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2003533. MTE:388. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  13. ^ a b c d e f g Salzer, Herbert E.; Johnson, Robert S.; Fettis, Henry E.; Caslin, James C.; Concus, Paul (July 1966). "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" (PDF). Mathematics of Computation. 20 (95): 469–471. doi:10.2307/2003630. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2003630. MTE:393. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  14. ^ a b Danos, Michael; Rafelski, Johann; Abramowitz, Milton; Stegun, Irene Ann, eds. (1984). Pocketbook of Mathematical Functions. Thun, Frankfurt/Main: Verlag Harri Deutsch. ISBN 978-3-87144-818-8. Retrieved 2016-03-13. (468 pages)
  15. ^ a b c d e Wrench, Jr., John William (April 1988). "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" (PDF). Mathematics of Computation. 50 (182): 646–647. doi:10.2307/2008636. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2008636. MSC:33-00,65A05. Archived (PDF) from the original on 2021-09-09. Retrieved 2016-03-13.
  16. ^ Zucker, Ruth (1983) [June 1964]. "Chapter 25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis". In Abramowitz, Milton; Stegun, Irene Ann (eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 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.
  17. ^ "Boole's Rule - from Wolfram MathWorld". Mathworld.wolfram.com. 2009-10-27. Archived from the original on 2021-12-01. Retrieved 2009-11-13.
  18. ^ Fettis, Henry E. (October 1969). "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" (PDF). Mathematics of Computation. 23 (108): 891. eISSN 1088-6842. ISSN 0025-5718. JSTOR 2004993. MTE:444. Archived (PDF) from the original on 2019-05-03. Retrieved 2016-03-13.
  19. ^ Davenport, James Harold (October 2002). "Table Errata 638: Abramowitz, M., & Stegun, I. Handbook of mathematical functions with formulas, graphs, and mathematical tables". Mathematics of Computation. 71 (240): 1801. eISSN 1088-6842. ISSN 0025-5718. JSTOR 4099976. MTE:638. PII:S0025-5718-97-00823-5. CODEN MCMPAF.

Further reading

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