Asymptotics of the hypergeometric function

被引：42
|
作者：
Jones, DS [1 ]
机构：
[1] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2001年 / 24卷 / 06期
关键词：
D O I：
10.1002/mma.208
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An asymptotic representation is obtained for the hypergeometric function F(a + lambda, b - lambda ,c, 1/2 - 1/2z) as \lambda\ --> infinity with \ph lambda\<<pi>. It is uniformly valid in the z-plane cut in an appropriate way. Several other forms of the hypergeometric function are discussed also. Another representation which has some advantages over the conventional one is given as well. Copyright (C) 2001 John Wiley & Sons, Ltd.
引用
收藏
页码：369 / 389
页数：21
相关论文
共 50 条
  • [21] Acceleration of generalized hypergeometric functions through precise remainder asymptotics
    Joshua L. Willis
    Numerical Algorithms, 2012, 59 : 447 - 485
  • [22] Plancherel-Rotach asymptotics for certain basic hypergeometric series
    Zhang, Ruiming
    ADVANCES IN MATHEMATICS, 2008, 217 (04) : 1588 - 1613
  • [23] On integral representations and asymptotics of some hypergeometric functions in two variables
    Wald, Sascha
    Henkel, Malte
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2018, 29 (02) : 95 - 112
  • [24] Asymptotics (p → ∞) of Lp-norms of hypergeometric orthogonal polynomials
    Dehesa, J. S.
    Guerrero, A.
    Lopez, J. L.
    Sanchez-Moreno, P.
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2014, 52 (01) : 283 - 300
  • [25] ZEROS OF HYPERGEOMETRIC FUNCTION
    RUNCKEL, HJ
    MATHEMATISCHE ANNALEN, 1971, 191 (01) : 53 - &
  • [26] CONFLUENT HYPERGEOMETRIC FUNCTION
    Nath, Pran
    SANKHYA, 1951, 11 : 153 - 166
  • [27] On the hypergeometric matrix function
    Jodar, L
    Cortes, JC
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 99 (1-2) : 205 - 217
  • [28] A HYPERGEOMETRIC FUNCTION TRANSFORM
    HIGGINS, TP
    JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1964, 12 (03): : 601 - 612
  • [29] A HYPERGEOMETRIC FUNCTION INTEGRAL
    GLASSER, ML
    SIAM REVIEW, 1986, 28 (04) : 573 - 573
  • [30] Gauss' hypergeometric function
    Beukers, Frits
    ARITHMETIC AND GEOMETRY AROUND HYPERGEOMETRIC FUNCTIONS, 2007, 260 : 23 - 42
12345