Asymptotics of the hypergeometric function

被引：46

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

页码：369 / 389

页数：21

共 7 条

[1] Rawlins' method and the diaphanous cone [J].

Jones, DS .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2000, 53 :91-109

[2]

MACDONALD HM, 1899, P LOND MATH SOC, V30, P169

[3]

Olver F. W. J., 1974, ASYMPTOTICS SPECIAL

[4] Diffraction by, or diffusion into, a penetrable wedge [J].

Rawlins, AD .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1987) :2655-2686

[5]

SZEGO G, 1933, P LOND MATH SOC, V36, P427

[6]

Watson G N, 1918, T CAMBRIDGE PHILOS S, V22, P277

[7]

Watson G. N., 1944, THEORY BESSEL FUNCTI

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