Abstract
A definite summation of hypergeometric terms of two variables is considered. Currently, for summation of such terms in computer algebra systems, a combination of the Zeilberger algorithm and the discrete Newton-Leibniz formula is used. As is known, the result of such summation is not always correct. In the paper, it is proposed to use simple preliminary examination of the term before applying the Zeilberger algorithm. If the hypergeometric term belongs to the class described in the paper, then the result obtained by the Zeilberger algorithm is correct or even there is no need to use it at all.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Maple online help, http://www.maplesoft.com/support/help
Zeilberger, D., The Method of Creative Telescoping, J. Symbolic Computation, 1991, vol. 11, pp. 195–204.
Petkovšek, M., Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficients, J. Symbolic Computation, 1992, vol. 14, pp. 243–264.
Abramov, S. and Petkovšsek, M., Gosper’s Algorithm, Accurate Summation, and the Discrete Newton-Leibniz Formula, Proc. of ISSAC’05, Beijing, 2005, pp. 5–12.
Abramov, S., Barkatou, M., van Hoeij, M., and Petkovšek, M., Subanalytic Solutions of Linear Difference Equations and Multidimensional Hypergeometric Sequences, J. Symbolic Computation (to appear).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Ryabenko, 2011, published in Programmirovanie, 2011, Vol. 37, No. 4.
Rights and permissions
About this article
Cite this article
Ryabenko, A.A. A definite summation of hypergeometric terms of special kind. Program Comput Soft 37, 187–191 (2011). https://doi.org/10.1134/S0361768811020083
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0361768811020083