A Generalization of Euler's Hypergeometric Transformation

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dc.creatorMaier, Robert S.
dc.date2003-02-08
dc.date2006-03-14
dc.date.accessioned2026-07-07T07:45:17Z
dc.date.available2026-07-07T07:45:17Z
dc.descriptionEuler'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.
dc.description19 pages, final (shortened) version, accepted by Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0302084
dc.identifierhttp://arxiv.org/abs/math/0302084
dc.identifierTrans. Amer. Math. Soc. 358 (2006), 39-57
dc.identifierdoi:10.1090/S0002-9947-05-04045-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123480
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.subject33C20, 33C05, 34M35, 05A19
dc.titleA Generalization of Euler's Hypergeometric Transformation
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