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Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. (English) Zbl 1108.05010

Summary: Algorithms for multi-sum summation and intergration of hypergeometric summands and integrands are given and sharp upper bounds for the orders are presented.

MSC:

05A15 Exact enumeration problems, generating functions
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References:

[1] Almkvist, G.; Zeilberger, D., The method of differentiating under the integral sign, J. Symbolic Comput., 10, 571-591 (1990) · Zbl 0717.33004
[2] W. Beckner, A. Regev, Unpublished, untitled, and undated manuscript, c. 1980; W. Beckner, A. Regev, Unpublished, untitled, and undated manuscript, c. 1980
[3] Macdonald, I. G., Some conjectures for root systems, SIAM J. Math. Anal., 13, 988-1007 (1982) · Zbl 0498.17006
[4] Mohammed, M.; Zeilberger, D., Sharp upper bounds for the orders of the recurrences outputted by the Zeilberger and \(q\)-Zeilberger algorithms, J. Symbolic Comput., 39, 201-207 (2005) · Zbl 1121.33023
[5] Paule, P., Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type, Electron. J. Combin., 1, R10 (1994) · Zbl 0814.05009
[6] Regev, A., Combinatorial sums, identities and trace identities of the \(2 \times 2\) matrices, Adv. Math., 46, 230-240 (1982) · Zbl 0499.16013
[7] Tefera, A., MultInt, a Maple package for multiple integration by the WZ method, J. Symbolic Comput., 34, 329-353 (2002) · Zbl 1015.33013
[8] Wilf, H. S.; Zeilberger, D., An algorithmic proof theory for hypergeometric (ordinary and “\(q\)”) multisum/integral identities, Invent. Math., 108, 575-633 (1992), [Available on-line from the authors’ websites] · Zbl 0739.05007
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