Algebraic transformations of Gauss hypergeometric functions

Details Algebraic transformations of Gauss hypergeometric functions Algebraic transformations of Gauss hypergeometric functions

2004-08-19

arxiv.org/abs/math/0408269v3

Funkcialaj Ekvacioj, 52 (2009), 139-180

Mathematics

Classical Analysis and ODEs

29 pages; 3 tables; Uniqueness claims and Remark 7.1 clarified by footnotes; formulas (28), (29) corrected

Scientific paper

This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function. The other transformations are considered more thoroughly in a series of supplementing articles.

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