REDUCE package for the indefinite and definite summation

Abstract

This article describes the REDUCE package ZEILBERG implemented by Gregor Stölting and the author which can be obtained from RedLib, accessible via anonymous ftp on ftp.zib-berlin.de in the directory pub/redlib/rules.The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of hypergeometric terms, respectively. An expression a k is called a hypergeometric term (or closed form ), if a k /a k-1 is a rational function with respect to k. Typical hypergeometric terms are ratios of products of powers, factorials, Γ function terms, binomial coefficients, and shifted factorials (Pochhammer symbols) that are integer-linear in their arguments.The package covers further extensions of both Gosper's and Zeilberger's algorithm which in particular are valid for ratios of products of powers, factorials, Γ function terms, binomial coefficients, and shifted factorials that are rational-linear in their arguments.A similar MAPLE package is described elsewhere [2].