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A generalization of Euler's hypergeometric transformation
2005
Transactions of the American Mathematical Society
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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
doi:10.1090/s0002-9947-05-04045-6
fatcat:6ikq6b2gbvebre2jrteveakew4