A finite sum representation of the Appell series F1(a, b, b′; c; x, y)

被引：9
|
作者：
Cuyt, A
Driver, K
Tan, J
Verdonk, B
机构：
[1] Univ Instelling Antwerp, Dept Math & Comp Sci, B-2610 Wilrijk, Belgium
[2] Univ Witwatersrand, Dept Math, ZA-2050 Johannesburg, South Africa
[3] Hefei Univ Technol, Inst Appl Math, Hefei 230009, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1999年 / 105卷 / 1-2期
关键词：
multiple hypergeometric function; Appell series; singularity;
D O I：
10.1016/S0377-0427(99)00035-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We use Picard's integral representation of the Appell series F-1(a, b, b'; c; x, y) for Re(a) > 0, Re(c - a) > 0 to obtain a finite sum algebraic representation of F-1 in the case when a, b, b' and c are positive integers with c > a. The series converges for \x\ < 1, \y\ < 1 and We show that F-1(a, b, b'; c; x, y) has two overlaying singularities at each of the points x = 1 and y = 1, one polar and one logarithmic in nature, when a, b, b', c is an element of N with c > a, (C) 1999 Elsevier Science B.V. All rights reserved.
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页码：213 / 219
页数：7
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