Dihedral Gauss hypergeometric functions

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.

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

References in corpus (5)

• Transformations of some Gauss hypergeometric functions
• Identities between Appell's and hypergeometric functions
• Degenerate Gauss hypergeometric functions
• A generalization of Clausen's identity
• Transformations and invariants for dihedral Gauss hypergeometric functions

Cited by in corpus (11)

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• Associated Legendre Functions and Spherical Harmonics of Fractional Degree and Order
• Transformations and invariants for dihedral Gauss hypergeometric functions
• On Some Hypergeometric Summations
• Character Vectors of Strongly Regular Vertex Operator Algebras
• A classification of coverings yielding Heun-to-hypergeometric reductions
• Darboux evaluations for hypergeometric functions with the projective monodromy PSL(2,F7)
• Dihedral evaluations of hypergeometric functions with the Kleinian projective monodromy
• Duality and Reciprocity for Hypergeometric Series with Gamma Product Formula
• The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processes