Handbook of Continued Fractions for Special Functions
作者： Haakon Waadeland , Annie A.M. Cuyt , Brigitte Verdonk , Vigdis Petersen , William B. Jones
DOI:
关键词: Digital Library of Mathematical Functions 、 Fraction (mathematics) 、 Special functions 、 Mathematical table 、 Library science 、 Application areas 、 Subject (documents) 、 Computer science
摘要: Special functions are pervasive in all fields of science and industry. The most well-known application areas physics, engineering, chemistry, computer statistics. Because their importance, several books websites (see for instance http: functions.wolfram.com) a large collection papers have been devoted to these functions. Of the standard work on subject, Handbook mathematical with formulas, graphs tables edited by Milton Abramowitz Irene Stegun, American National Institute Standards claims sold over 700 000 copies! But so far no project has systematic study continued fraction representations This handbook is result such an endeavour. We emphasise that only 10% fractions contained this book, can also be found Stegun or at Wolfram website!
amazon.com
openlibrary.org参考文章(23)
Wolfgang J. Thron, A Priori Truncation Error Estimates for Stieltjes Fractions E. B. Christoffel. pp. 203- 211 ,(1981) , 10.1007/978-3-0348-5452-8_12
H.S. Wall, Analytic Theory of Continued Fractions ,(1967)
Alfred van der Poorten, A Proof that Euler Missed … Pi: A Source Book. ,vol. 1, pp. 439- 447 ,(2000) , 10.1007/978-1-4757-3240-5_49
Vladimir N. Sorokin, Jeannette Van Iseghem, Matrix Continued Fractions Journal of Approximation Theory. ,vol. 96, pp. 237- 257 ,(1999) , 10.1006/JATH.1998.3232
Robert Spira, Calculation of the Gamma Function by Stirling's Formula Mathematics of Computation. ,vol. 25, pp. 317- 322 ,(1971) , 10.1090/S0025-5718-1971-0295539-6
W. J. Thron, H. Waadeland, Accelerating convergence of limit periodic continued fractionsK(an/1) Numerische Mathematik. ,vol. 34, pp. 155- 170 ,(1980) , 10.1007/BF01396057
Marietta J. Tretter, G. W. Walster, Analytic Subtraction Applied to the Incomplete Gamma and Beta Functions SIAM Journal on Scientific and Statistical Computing. ,vol. 1, pp. 321- 326 ,(1980) , 10.1137/0901022
Jet Wimp, Bernhard Beckermann, Families of two-point Pade´ approximants and some 4 F 3 (1) identities Siam Journal on Mathematical Analysis. ,vol. 26, pp. 761- 773 ,(1995) , 10.1137/S0036141091223492
N. M. Temme, The numerical computation of the confluent hypergeometric functionU(a, b, z) Numerische Mathematik. ,vol. 41, pp. 63- 82 ,(1983) , 10.1007/BF01396306
E. T. Whittaker, G. N. Watson, A Course of Modern Analysis ,(1902)