Euler's transformation formula for the Gauss hypergeometric function 2F 1 is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but not linearly. Its consequences for hypergeometric summation are explored. It has as a corollary a summation formula of Slater. From this formula new one-term evaluations of 2F 1 (-1) and 3F 2(1) are derived by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of 2F 1(-1) with linearly constrained parameters are derived as well.
ASJC Scopus subject areas
- Applied Mathematics