A HOLONOMIC SYSTEMS-APPROACH TO SPECIAL-FUNCTIONS IDENTITIES

被引：263

作者：

ZEILBERGER, D ^{[1
]}

机构：

[1] TEMPLE UNIV,DEPT MATH,PHILADELPHIA,PA 19122

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1990年 / 32卷 / 03期

基金：

美国国家科学基金会;

关键词：

computer algebra; Elimination; hypergeometric series; partial difference operators; Weyl algebra;

D O I：

10.1016/0377-0427(90)90042-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We observe that many special functions are solutions of so-called holonomic systems. Bernstein's deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps. This is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE. © 1990.

引用

页码：321 / 368

页数：48