Transformations and invariants for dihedral Gauss hypergeometric functions

Details Transformations and invariants for dihedral Gauss hypergeometric functions Transformations and invariants for dihedral Gauss hypergeometric functions

2011-01-19

arxiv.org/abs/1101.3688v1

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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.

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