000 02316cam a2200289 a 4500
001 3088481
005 20250611141428.0
008 980520s1999 enk b 001 0 eng
020 _a9780521789882
040 _aCSL
_cCSL
041 _2eng
_aeng
084 _aB39 N9 NBHM
_qCSL
100 1 _aAndrews, George E.,
_eauthor.
_9408575
245 1 0 _aSpecial functions
260 _aCambridge :
_bCambridge University Press,
_c1999.
300 _axvi, 664 p. ;
_c25 cm.
440 0 _aEncyclopedia of mathematics and its applications ;
_v71
_9812603
504 _aIncludes bibliographical references (p. 641-653) and indexes.
520 _aSpecial functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.
650 0 _aFunctions, Special.
_9812470
650 0 _aGamma and Beta Functions
_9812604
650 0 _aHypergeometric Functions
650 0 _aOrthogonal Polynomials
_9812472
700 1 _aAskey, Richard.
_eco-author.
_9812605
700 1 _aRoy, Ranjan,
_eco-author.
_9212009
942 _2CC
_n0
_cTEXL
_hB39 N9 NBHM
999 _c1431611
_d1431611