Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7)

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.

Coordinated with arxiv:1809.01502; 37 pages, 2 tables

References in corpus (5)

• Transformations of some Gauss hypergeometric functions
• Algebraic transformations of Gauss hypergeometric functions
• Dihedral Gauss hypergeometric functions
• Algebraic Hypergeometric Transformations of Modular Origin
• Dihedral evaluations of hypergeometric functions with the Kleinian projective monodromy