Extended symmetric Pascal matrices via hypergeometric functions

被引：6

作者：

Cheon, GS ^{[1
]}

El-Mikkawy, M

机构：

[1] Daejin Univ, Dept Math, Pocheon 487711, South Korea

[2] Mansoura Univ, Dept Math, Mansoura 35516, Egypt

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2004年 / 158卷 / 01期

关键词：

Cholesky factorization; Pascal matrix; hypergeometric function; Legendre polynomial; Delannoy number;

D O I：

10.1016/j.amc.2003.08.095

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we give a matrix representation of the hypergeometric functions of the type F-2(1) (a, b; c; x). As a result, we obtain a connection between the hypergeometric functions, the Legendre polynomials and the Delannoy numbers. Moreover, it is shown that each entry of P-n(x, y)P-n(x, y)(T) can be represented by the hypergeometric functions where [P-n(x, y)](ij) = x(i-j)y(i+j-2) ((i - 1)(j - 1)) is the extended generalized Pascal matrix which is defined by Zhang and Liu [Linear Algebra Appl. 271 (1998) 169]. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：159 / 168

页数：10

共 8 条

[1] The linear algebra of the generalized Pascal functional matrix [J].