zbMATH — the first resource for mathematics

MultInt, a MAPLE package for multiple integration by the WZ method. (English) Zbl 1015.33013
Starting from the MAPLE implementation TRIPLE INTEGRAL written by D. Zeilberger to describe the WZ-method [see H. S. Wilf and D. Zeilberger, Invent. Math. 103, No 3, 575-634 (1992; Zbl 0782.05009); see also the preview Zbl 0739.05007)] for the case of three continuous variables, the author in the present paper describes a MAPLE package MultInt which improves and generalizes Zeilberger’s TRIPLE INTEGRAL for any specific number of continuous variables so that it completely implements the continuous version of the multi-WZ method. Several examples showing how this package MultInt can be used to generate proofs of identities (or recurrences) involving multiple integrals of proper-hyperexponential functions, are also given.

33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
65Y15 Packaged methods for numerical algorithms
68W30 Symbolic computation and algebraic computation
qZeil; Maple; MultInt
Full Text: DOI
[1] Andrews, G., Q-series: their development and applications in analysis, number theory, combinatorics, physics, and computer algebra, CBMS series 59, (1986), AMS Providence, RI
[2] Andrews, G.; Askey, R.; Roy, R., Special functions, (1998), Cambridge University Press
[3] Andrews, G.E.; Paule, P., A higher degree binomial coefficient identity, Am. math. monthly, 99, 64, (1992)
[4] Andrews, G.E.; Paule, P., Some questions concerning computer-generated proofs of a binomial double-sum identity, J. symb. comput., 16, 147-153, (1993) · Zbl 0836.05003
[5] Böing, H.; Koepf, W., Algorithms for q -hypergeometric summation in computer algebra, J. symb. comput., 28, 777-799, (1999) · Zbl 0946.65008
[6] Carlitz, L., Summations of products of binomial coefficients, Am. math. monthly, 75, 906-908, (1968)
[7] F. Chyzak, London Math. Society Lecture Note Series 251, 1998, 32, 60
[8] Egorychev, G.P., Integral representation and the computation of combinatorial sums, (1984), AMS Providence, RI · Zbl 0524.05001
[9] Ekhad, S.B., A one-line proof of the habsieger – zeilberger G2constant term identity, J. comput. appl. math., 34, 133-134, (1991) · Zbl 0737.33010
[10] Good, I.J., Short proof of a conjecture by Dyson, J. math. phys., 11, 1884, (1970)
[11] Habsieger, L., La q-conjecture de macdonald – morries pour G2, C. R. acad. sci. Paris Sér. I math, 303, 211-213, (1986) · Zbl 0598.05006
[12] Koornwinder, T.H., On zeilberger’s algorithm and its q -analogue, J. symb. comput., 16, 147-153, (1992)
[13] Macdonald, I.G., Some conjectures for root systems, SIAM J. math. anal., 13, 988-1007, (1982) · Zbl 0498.17006
[14] W. G. Morris, 1982
[15] Paule, P.; Riese, A., A Mathematica q -analogue of zeilberger’s algorithms based on an algebraically motivated approach to q-hypergeometric telescoping, (), 179-210 · Zbl 0869.33010
[16] Petkovšek, M.; Wilf, H.S.; Zeilberger, D., A=B, (1996), A. K. Peters Wellesley, MA
[17] Riese, A., Fine-tuning zeilberger’s algorithm: the methods of automatic filtering and creative substituting, (), 243-254 · Zbl 1037.33018
[18] Selberg, A., Bemerkninger om et multipelt integral, Norsk math. tidsskr, 26, 71-78, (1944)
[19] Strehl, A., Binomial identities—combinatorial and algorithmical aspects, Discrete math., 136, 309-346, (1994) · Zbl 0823.33003
[20] Tefera, A., A multiple integral evaluation inspired by the multi-WZ method, Electron. J. combinatorics, 6, N2, (1999) · Zbl 0939.65035
[21] K. Wegschaider, 1997
[22] Wilf, H.S.; Zeilberger, D., An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities, Invent. math., 108, 575-633, (1992) · Zbl 0739.05007
[23] Zeilberger, D., A proof of the G2case of macdonald’s root system – dyson conjecture, SIAM J. math. anal., 18, 880-883, (1987) · Zbl 0643.05004
[24] Zeilberger, D., A fast algorithm for proving terminating hypergeometric identities, Discrete math., 80, 207-211, (1990) · Zbl 0701.05001
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.