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

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 have already been considered for algebraic 2 F 1 -functions. This article presents Darboux evaluations for the classical case of 3 F 2 -functions with the projective monodromy group PSL (2 , F 7) . The pullback curves are of genus 0 (in the simplest case) or of genus 1. As an application of the genus 0 evaluations, appealing modular evaluations of the same 3 F 2 -functions are derived. [ABSTRACT FROM AUTHOR]