REDUCE package for the indefinite and definite summation

1994/12/17 by Wolfram Koepf, Koepf, Wolfram
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.math/9412228

arxiv created 1994/12/17 · arxiv updated 2009/11/30

Abstract

This article describes the REDUCE package ZEILBERG implemented by Gregor Stölting and the author. 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 \sl hypergeometric term (or \sl 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.

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• Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
• Software for the Algorithmic Work with Orthogonal Polynomials and Special Functions
• The Extended Zeilberger's Algorithm with Parameters
• On two-term hypergeometric recursions with free lower parameters