Generating functionology
A fast algorithm for proving terminating hypergeometric identities
Discrete Mathematics
The method of creative telescoping
Journal of Symbolic Computation
On Zeilberger's algorithm and its q-analogue
VII SPOA Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Computer algebra handbook
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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 ak is called a hypergeometric term (or closed form), if ak/ak-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].