Computer generation of complicated transformations and reduction formulas for multiple hypergeometric series

Abstract

Universal transformation formulas for multiple hypergeometric series obtained recently with the help of operator factorization method have been used to develop an effective software greatly surpassing in this regard all available computer algebra programs. An application of the transformations to derivation of reduction formulas is given. To this end an algorithmic criterion for finding reducible cases was put forward. The criterion holds that any non-trivial reduction formula for a multiple series is a corollary of a trivial (self-obvious) reduction for an appropriately transformed series. The striking effectiveness of the algorithm is illustrated by impressive examples relating to Gel'fand series in 3 and 4 variables connected with the Grassmanians G 2,4 and G 3,6 , respectively.