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. Pull-back transformations for the dihedral hypergeometric equations are also presented, including Klein' s pullback transformations for the equations with a finite (dihedral) monodromy group.