A definite summation of hypergeometric terms of special kind
Tóm tắt
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.
Tài liệu tham khảo
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).