CONTIGUITY RELATIONS FOR GENERALIZED HYPERGEOMETRIC-FUNCTIONS

It is well known that the hypergeometric functions F-2(1)(alpha +/- 1, beta, gamma; t) F-2(1)(alpha, beta +/- 1, gamma; t), F-2(1)(alpha, beta, gamma +/- 1; t), which are contiguous to F-2(1)(alpha, beta, gamma; t), can be expressed in terms of F-2(1)(alpha, beta, gamma; t) and F-2(1)'(alpha, beta, gamma; t). We explain how to derive analogous formulas for generalized hypergeometric functions. Our main point is that such relations can be deduced from the geometry of the cone associated in a recent paper by B. Dwork and F. Loeser to a generalized hypergeometric series.