Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions

被引：9

作者：

Gautschi, W ^{[1
]}

机构：

[1] Purdue Univ, Dept Comp Sci, W Lafayette, IN 47907 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2002年 / 139卷 / 01期

关键词：

D O I：

10.1016/S0377-0427(01)00383-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Integral representations of hypergeometric and confluent hypergeometric functions with real parameters and complex arguments are used to approximate these functions by Gaussian quadrature. An analysis is given of the errors involved and of estimates of the number of Gauss points required to achieve any given accuracy. Numerical examples illustrate the theory. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：173 / 187

页数：15

共 50 条

[31] Transformations of some Gauss hypergeometric functions
Vidunas, R
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 178 (1-2) : 473 - 487
[32] EXPANSION OF THE HYPERGEOMETRIC FUNCTIONS IN SERIES OF CONFLUENT ONES
TRICOMI, FG
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 57 (01) : 80 - 80
[33] On some identities for confluent hypergeometric functions and Bessel functions
Okuyama, Yoshitaka
[J]. JOURNAL OF APPROXIMATION THEORY, 2024, 298
[34] Extended Gauss Hypergeometric Matrix Functions
Abdalla, Mohamed
Bakhet, A.
[J]. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2018, 42 (A3): : 1465 - 1470
[35] Extended Gauss Hypergeometric Matrix Functions
Mohamed Abdalla
A. Bakhet
[J]. Iranian Journal of Science and Technology, Transactions A: Science, 2018, 42 : 1465 - 1470
[36] Algebraic Transformations of Gauss Hypergeometric Functions
Vidunas, Raimundas
[J]. FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2009, 52 (02): : 139 - 180
[37] Monodromies at infinity of confluent A-hypergeometric functions
Ando, Kama
Esteroy, Alexander
Takeuchi, Kiyoshi
[J]. ADVANCES IN MATHEMATICS, 2015, 272 : 1 - 19
[38] CONFLUENT HYPERGEOMETRIC-FUNCTIONS ON AN EXCEPTIONAL DOMAIN
NAGAOKA, S
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1984, 60 (06) : 218 - 220
[39] Generating functions for the generalized Gauss hypergeometric functions
Srivastava, H. M.
Agarwal, Praveen
Jain, Shilpi
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 247 : 348 - 352
[40] INTEGRALS OF 2 CONFLUENT HYPERGEOMETRIC-FUNCTIONS
KARULE, E
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (11): : 1969 - 1971

← 1 2 3 4 5 →