Dihedral Gauss hypergeometric functions
Classical Analysis and ODEs
2013-10-04 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.0807.4888,
title = {Dihedral Gauss hypergeometric functions},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:0807.4888},
year = {2013}
}
Comments
28 pages; trigonometric expressions added; transformations and invariants moved to arxiv.org/1101.3688