Linear transformations and reduction formulas for the Gelfand hypergeometric functions associated with the Grassmannians \(G_{2,4}\) and \(G_{3,6}\) (Q1397323)

This is a continuation of the work of the first author [Mat. Zametki 67, 573-581 (2000; Zbl 0954.33006); ibid. 70, 769-779 (2001; Zbl 1027.33013)]. These papers need to be referred to for the definitions of various notations. Several interesting new reduction formulas are derived for the Gelfand hypergeometric functions associated with the Grassmannians \(G_{2,4}\) and \(G_{3,6}\). The derivations are based upon finding a combination of linear transformations of a series in order to reduce it to a form suitable for the application of simple reduction formulas. In order to obtain these results, a program for symbolic transformations of multiple hypergeometric series was developed as a shell over the computer algebra system Maple V-4.