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

Vidunas, Raimundas

doi:10.1007/s11139-019-00229-x

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

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Vidunas, Raimundas
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s11139-019-00229-x
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Citation

Vidunas, R. (2020). Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7). The Ramanujan Journal, 53(1), 85-121. doi:10.1007/s11139-019-00229-x.

Cite as: https://hdl.handle.net/21.11116/0000-0008-A9EA-2

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.