Apagodu, Moa; Zeilberger, Doron Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. (English) Zbl 1108.05010 Adv. Appl. Math. 37, No. 2, 139-152 (2006). Summary: Algorithms for multi-sum summation and intergration of hypergeometric summands and integrands are given and sharp upper bounds for the orders are presented. Cited in 4 ReviewsCited in 54 Documents MSC: 05A15 Exact enumeration problems, generating functions Keywords:multi-sum summation; hypergeometric summands and integrands Software:qZEILBERGER; MultiZeilberger; ZEILBERGER; DEtools; MultInt; NewZeil.m PDFBibTeX XMLCite \textit{M. Apagodu} and \textit{D. Zeilberger}, Adv. Appl. Math. 37, No. 2, 139--152 (2006; Zbl 1108.05010) Full Text: DOI 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under the integral sign, J. Symbolic Comput., 10, 571-591 (1990) · Zbl 0717.33004 [2] W. Beckner, A. Regev, Unpublished, untitled, and undated manuscript, c. 1980; W. Beckner, A. Regev, Unpublished, untitled, and undated manuscript, c. 1980 [3] Macdonald, I. G., Some conjectures for root systems, SIAM J. Math.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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.