A prototype software system is being developed for computing with definite summations which incorporates as many as possible, in the allotted time, of the useful methods for recognizing and simplifying infinite (more generally, definite) sums. Some of these methods, whether or not they succeed in finding a closed form, optionally offer an alternative expression, mathematically equivalent to the sum but more rapidly convergent.A secondary goal is to develop in parallel the complementary process of expanding expressions into infinite series. Researchers are emphasizing (generalized) hypergeometric series, which include binomial coefficient and (most) power series, the sums most frequently encountered by students and researchers. At least some q-series and numerous infinite products are being attacked. The primary mechanism manipulates and combines tabulated summands into agreement with the query summand. A sufficient repertoire of these manipulations and combinations will handle vastly more sums than could any published table or simple database.Commercial Applications:The Commercial exploitation of the technology in the Macsyma mathematics software product is virtually assured. Macsyma is a well-established symbolic-numerical mathematics software system with many users who will benefit from better technology for computing with summations and series.
