Algebraic transformations of Gauss hypergeometric functions

Abstract

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.

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

References in corpus (2)

• Transformations of some Gauss hypergeometric functions
• Degenerate Gauss hypergeometric functions

Cited by in corpus (10)

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• Dihedral evaluations of hypergeometric functions with the Kleinian projective monodromy
• Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7)
• Periods of Hodge cycles and special values of the Gauss' hypergeometric function