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＜E-Book＞
Handbook of Continued Fractions for Special Functions / by Annie A.M. Cuyt, Vigdis Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones

Edition	1st ed. 2008.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	2008
Language	English
Size	XVI, 431 p : online resource
Authors	*Cuyt, Annie A.M author Petersen, Vigdis author Verdonk, Brigitte author Waadeland, Haakon author Jones, William B author SpringerLink (Online service)
Subjects	LCSH:Special functions LCSH:Engineering mathematics LCSH:Engineering -- Data processing  All Subject Search LCSH:Mathematics LCSH:Computer science -- Mathematics  All Subject Search LCSH:Engineering LCSH:Social sciences LCSH:Humanities FREE:Special Functions FREE:Mathematical and Computational Engineering Applications FREE:Mathematics FREE:Mathematics of Computing FREE:Technology and Engineering FREE:Humanities and Social Sciences
Notes	Basic Theory -- Basics -- Continued fraction representation of functions -- Convergence criteria -- Padé approximants -- Moment theory and orthogonal functions -- Numerics -- Continued fraction construction -- Truncation error bounds -- Continued fraction evaluation -- Special Functions -- On tables and graphs -- Mathematical constants -- Elementary functions -- Gamma function and related functions -- Error function and related integrals -- Exponential integrals and related functions -- Hypergeometric functions -- Confluent hypergeometric functions -- Bessel functions -- Probability functions -- Basic hypergeometric functions Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, namely the Handbook of Mathematical Functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website! HTTP:URL=https://doi.org/10.1007/978-1-4020-6949-9

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