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Mathematics, Classical Analysis and ODEs
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.
