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A definite summation of hypergeometric terms of special kind

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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.

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References

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    A. A. Ryabenko

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  1. A. A. Ryabenko
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Correspondence to A. A. Ryabenko.

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Original Russian Text © A.A. Ryabenko, 2011, published in Programmirovanie, 2011, Vol. 37, No. 4.

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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

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  • DOI: https://doi.org/10.1134/S0361768811020083

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