A Generalization of Euler's Hypergeometric Transformation

Details A Generalization of Euler's Hypergeometric Transformation A Generalization of Euler's Hypergeometric Transformation

2003-02-08

arxiv.org/abs/math/0302084v4

Trans. Amer. Math. Soc. 358 (2006), 39-57

Mathematics

Classical Analysis and ODEs

19 pages, final (shortened) version, accepted by Trans. Amer. Math. Soc

Scientific paper

10.1090/S0002-9947-05-04045-6

Euler's transformation formula for the Gauss hypergeometric function 2F1 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 corollary a summation formula of Slater. From this formula new one-term evaluations of 2F1(-1) and 3F2(1) are derived, by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of 2F1(-1) with linearly constrained parameters are derived as well.

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