Mathematics – Classical Analysis and ODEs
Scientific paper
2003-02-08
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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