Darboux evaluations of algebraic Gauss hypergeometric functions
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.
Keywords
Cite
@article{arxiv.math/0504264,
title = {Darboux evaluations of algebraic Gauss hypergeometric functions},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:math/0504264},
year = {2012}
}
Comments
The list of seed hypergeometric evaluations (in Section 2) reduced by half; uniqueness claims explained; 34 pages; Kyushu Journal of Mathematics, 2013