Mohammed, Mohamud; Zeilberger, Doron Sharp upper bounds for the orders of the recurrences output by the Zeilberger and \(q\)-Zeilberger algorithms. (English) Zbl 1121.33023 J. Symb. Comput. 39, No. 2, 201-207 (2005). Summary: We do what the title promises, and as a bonus, we get much simplified versions of these algorithms, that do not make any explicit mention of Gosper’s algorithm. Cited in 13 Documents MSC: 33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) 65Q05 Numerical methods for functional equations (MSC2000) Keywords:Symbolic summation; \(q\)-analog; hypergeometric functions Software:NewZeil.m; qZeil; ZEILBERGER; qZEILBERGER PDFBibTeX XMLCite \textit{M. Mohammed} and \textit{D. Zeilberger}, J. Symb. Comput. 39, No. 2, 201--207 (2005; Zbl 1121.33023) Full Text: DOI References: [1] Abramov, S. A., When does Zeilberger’s algorithm succeed?, Adv. Appl. Math., 30, 424-441 (2003) · Zbl 1030.33011 [2] Chen, B.; Hou, Q.; Mu, Y., Applicability of the \(q\)-analogue of Zeilberger’s algorithm (preprint) (2004), Available online from [3] Gosper, R. W., Decision procedures for indefinite hypergeometric summation, Proc. Natl. Acad. Sci. USA, 75, 40-42 (1975) · Zbl 0384.40001 [4] Koepf, W., Hypergeometric Summation (1998), Vieweg [5] Koornwinder, T. H., On Zeilberger’s algorithm and its \(q\)-analog, J. Comput. Appl. Math., 48, 91-111 (1993) · Zbl 0797.65011 [6] Paule, P.; Riese, A., A Mathematica \(q\)-analog of Zeilberger’s algorithm based on an algebraically motivated approach to \(q\)-hypergeometric telescoping, (Special Functions, \(q\)-series and Related Topics. Special Functions, \(q\)-series and Related Topics, Fields Inst. Comm., vol. 14 (1997), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 179-210 · Zbl 0869.33010 [7] Paule, P.; Schorn, M., A Mathematica version of Zeilberger’s algorithm for proving binomial coefficients identities, J. Symbolic Comput., 20, 673-698 (1995) · Zbl 0851.68052 [8] Petkovsek, M.; Wilf, H. S.; Zeilberger, D., \(A = B (1996)\), AK Peters, Wellesley, Available on-line from the authors’ Web sites [9] 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’ Web sites · Zbl 0739.05007 [10] Zeilberger, D., A fast algorithm for proving terminating hypergeometric identities, Discrete Math., 80, 207-211 (1990), Available on-line from the author’s Web site · Zbl 0701.05001 [11] Zeilberger, D., The method of creative telescoping, J. Symbolic Comput., 11, 195-204 (1991) · Zbl 0738.33002 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.