Transformations and invariants for dihedral Gauss hypergeometric functions

Abstract

Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums. Besides, pull-back transformations for the dihedral hypergeometric equations are presented, including Klein's pullback transformations for the equations with a finite (dihedral) monodromy group.

29 pages; a split off from arxiv.org/0807.4888

References in corpus (5)

• The 192 Solutions of the Heun Equation
• Identities between Appell's and hypergeometric functions
• Dihedral Gauss hypergeometric functions
• A generalization of Clausen's identity
• Transformations of algebraic Gauss hypergeometric functions

Cited by in corpus (5)

• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Dihedral Gauss hypergeometric functions
• A generalization of Clausen's identity
• Algorithms and differential relations for Belyi functions
• A classification of coverings yielding Heun-to-hypergeometric reductions