Dihedral Gauss hypergeometric functions

Details Dihedral Gauss hypergeometric functions Dihedral Gauss hypergeometric functions

2008-07-30

arxiv.org/abs/0807.4888v3

Kyushu Journal of Mathematics, 2011

Mathematics

Classical Analysis and ODEs

28 pages; trigonometric expressions added; transformations and invariants moved to arxiv.org/1101.3688

Scientific paper

Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument variable. The paper presents general elementary expressions of these dihedral hypergeometric functions, involving finite bivariate sums expressible as terminating Appell's F2 or F3 series. Additionally, trigonometric expressions for the dihedral functions are presented, and degenerate cases (logarithmic, or with the monodromy group Z/2Z) are considered.

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