English

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.

Keywords

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

R2 v1 2026-06-23T03:32:58.484Z