On a connection between symmetric polynomials, generalized Stirling numbers and the Newton general divided difference interpolation polynomial

被引：9

作者：

El-Mikkawy, M ^{[1
]}

El-Desouky, B

机构：

[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

[2] Suez Canal Univ, Fac Educ, Dept Math, Port Said, Egypt

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2003年 / 138卷 / 2-3期

关键词：

Stirling numbers; interpolation; symmetric polynomials; matrices; MAPLE programming;

D O I：

10.1016/S0096-3003(02)00142-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper gives a connection between symmetric polynomials, generalized Stirling numbers and the Newton general divided difference interpolation polynomial. The generalized Stirling numbers of the first and second kind denoted s(n,k)([a]) and S-n,k([a]) respectively are given symbolically for the case n = 5, as an illustrative example, by using MAPLE programming [MAPLE V R3 Programming Reference Manual]. These numbers depend on n, k and n distinct values a(1), a(2).... a(n). The ordinary Stirling numbers s(n,k) and S-n,S-k may be obtained as special cases by taking a(i) = i - 1, i = 1 (1) n. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：375 / 385

页数：11