Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7)
Classical Analysis and ODEs
2020-12-29 v2
Abstract
Algebraic hypergeometric functions can be compactly expressed as radical functions on pull-back curves where the monodromy group is simpler, say, a finite cyclic group. These so-called Darboux evaluations were already considered for algebraic 2F1-functions. This article presents Darboux evaluations for the classical case of 3F2-functions with the projective monodromy group PSL(2,F7). As an application, appealing modular evaluations of the same 3F2-functions are derived.
Cite
@article{arxiv.1808.04524,
title = {Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7)},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:1808.04524},
year = {2020}
}
Comments
Coordinated with arxiv:1809.01502; 37 pages, 2 tables