Abstract
In the paper, an implementation in the computer algebra system Maple of an approach to summation based on hypergeometric pattern matching is considered. In spite of a number of existing modern summation algorithms, this approach remains to be valuable, since, if applicable, it allows one to find the result much faster than other approaches. The implementation is performed in the form of package Pattern Matching Summation. The structure of the package, pattern representation, possibility of extending the list of patterns, and matching mechanism are described. Examples of using the package are presented. Specific features of using summation formulas from handbooks as the patterns are considered. To obtain correct results, additional analysis is often required to determine the cases where the given formula is applicable.
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Petkovšek, M., Wilf, H.S., and Zeilberger, D.A., A=B, A K Peters, 1996.
Gosper, R.W., Jr., Indefinite Hypergeometric Sums in MACSYMA, Proc. of the MACSYMA User’s Conf., Berkeley, CA, 1977, pp. 237–251.
Karr, M., Summation in Finite Terms, J. ACM, 1981, vol. 28, no. 2, pp. 305–350.
Krattenthaller, C., HYP and HYPQ, J. Symbolic Computations, 1995, vol. 20, pp. 737–744.
Krattenthaller, C., HYP, Manual for a Mathematica Package for Handling Hypergeometric Series. http://www.mat.univie.ac.at/~kratt/hyp-hypq/hyp.html. 1994.
Gauthier, B., HYPERG, Maple Package, User’s Reference Manual. http://www.igm.univ-mlv.fr/~gautier/HYPERG.html. 1999.
Khmelnov, D.E. and Ryabenko, A.A., Pattern Matching Summation in MAPLE, MMCP’2009: Book of Abstracts of the Int. Conf., Dubna: JINR, 2009, pp. 143–144.
Gradshtein, I.S. and Ryzhik, I.M., Tablitsi integralov, sum, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Fizmatgiz, 1963, 4th ed.
Graham, R., Knuth, D.E., and Patashnik, O., Concrete Mathematics, Reading, Mass.: Addison-Wesley, 1994, 2nd ed.
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Original Russian Text © A.A. Ryabenko, D.E. Khmelnov, 2010, published in Programmirovanie, 2010, Vol. 36, No. 2.
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Ryabenko, A.A., Khmelnov, D.E. Hypergeometric pattern matching summation in maple. Program Comput Soft 36, 87–96 (2010). https://doi.org/10.1134/S0361768810020064
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DOI: https://doi.org/10.1134/S0361768810020064