• Source: Abramowitz and Stegun

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.




Overview


Since it was first published in 1964, the 1046-page Handbook has been one of the most comprehensive sources of information on special functions, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of applied mathematics. The notation used in the Handbook is the de facto standard for much of applied mathematics today.
At the time of its publication, the Handbook was an essential resource for practitioners. Nowadays, computer algebra systems have replaced the function tables, but the Handbook remains an important reference source. The foreword discusses a meeting in 1954 in which it was agreed that "the advent of high-speed computing equipment changed the task of table making but definitely did not remove the need for tables".

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 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.

The chapters are:

Mathematical Constants
Physical Constants and Conversion Factors
Elementary Analytical Methods
Elementary Transcendental Functions
Exponential Integral and Related Functions
Gamma Function and Related Functions
Error Function and Fresnel Integrals
Legendre Functions
Bessel Functions of Integral Order
Bessel Functions of Fractional Order
Integrals of Bessel Functions
Struve Functions and Related Functions
Confluent Hypergeometric Functions
Coulomb Wave Functions
Hypergeometric Functions
Jacobian Elliptic Functions and Theta Functions
Elliptic Integrals
Weierstrass Elliptic and Related Functions
Parabolic Cylinder Functions
Mathieu Functions
Spheroidal Wave Functions
Orthogonal Polynomials
Bernoulli and Euler Polynomials, Riemann Zeta Function
Combinatorial Analysis
Numerical Interpolation, Differentiation, and Integration
Probability Functions
Miscellaneous Functions
Scales of Notation
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:
2nd printing with corrections: November 1964; errata:
3rd printing with corrections: March 1965; errata:
4th printing with corrections: December 1965; errata:
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)




Related projects


Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum, which, by this time, could be easily calculated with scientific pocket calculators. The references were removed as well. Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter. The numbering of formulas was kept for easier cross-reference.
A digital successor to the Handbook, long under development at NIST, was released as the “Digital Library of Mathematical Functions” (DLMF) on 11 May 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press.




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
Numerical analysis
Rubber book, a Handbook of Chemistry & Physics
Reference book
Handbook
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
Louis Melville Milne-Thomson, author of the book chapters on 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
Boole's rule, a mathematical rule of integration sometimes known as Bode's rule, due to a typo in Abramowitz and Stegun (1972, p. 886) that was subsequently propagated.
On-Line Encyclopedia of Integer Sequences




Notes






References






Further reading


Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. 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. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
Boisvert, Ronald F.; Lozier, Daniel W. (January 2001). "Handbook of Mathematical Functions" (PDF). In Lide, David R. (ed.). 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. ISBN 978-0-8493-1247-2. CODEN NSPUE2. NIST Special Publication 958. 20402–9325. Archived from the original (PDF) on 2011-10-14. Retrieved 2016-03-13. (NB. A history of the activities leading up to and surrounding the development of the Handbook.)




External links


A high quality scan of the book, in PDF and TIFF formats, hosted at the University of Birmingham, UK
The book in scanned format, now hosted at 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.
Another scanned version by ConvertIt.com
numerical.recipes download - NBS, Tenth Printing, December 1972, with Corrections - PDF without Search
NIST Digital Library of Mathematical Functions, the digital successor of the Handbook

Kata Kunci Pencarian:

• Tabel matematika
• Daftar identitas trigonometri
• Diferensiasi fungsi trigonometri
• Distribusi khi-kuadrat
• Tabel pencarian
• Distribusi F
• Fungsi integral logaritmik
• Akar kuadrat
• Fungsi gamma
• Logaritma
• Abramowitz and Stegun
• Bessel function
• List of trigonometric identities
• Irene Stegun
• Milton Abramowitz
• Exponential integral
• Disk (mathematics)
• Helmholtz equation
• Falling and rising factorials
• Mathematical table