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Darboux evaluations of algebraic Gauss hypergeometric functions

Raimundas Vidunas
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Abstract

This paper presents explicit expressions for algebraic Gauss hypergeometric functions. We consider solutions of hypergeometric equations with the tetrahedral, octahedral and icosahedral monodromy groups. Conceptually, we pull-back such a hypergeometric equation onto its Darboux curve so that the pull-backed equation has a cyclic monodromy group. Minimal degree of the pull-back coverings is 4, 6 or 12 (for the three monodromy groups, respectively). In explicit terms, we replace the independent variable by a rational function of degree 4, 6 or 12, and transform hypergeometric functions to radical functions.

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Raimundas Vidunas. 2012-09-07. Darboux evaluations of algebraic Gauss hypergeometric functions. https://arxiv.org/abs/math/0504264

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