Hypergeometric pattern matching summation in maple

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.