Degenerate and dihedral Heun functions with parameters

2013/09/29 by Vidunas, Raimundas
#33C05 #33E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.7656

Abstract

Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, "elementary") functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric equations with Liouvillian solutions. This paper presents the Liouvillian solutions of Heun's equations that are pull-backs of the parametric hypergeometric equations with cyclic or dihedral monodromy groups.

Related

• Transformations of algebraic Gauss hypergeometric functions
• Darboux evaluations of algebraic Gauss hypergeometric functions
• Heun equations coming from geometry
• A classification of coverings yielding Heun-to-hypergeometric reductions
• On reducing the Heun equation to the hypergeometric equation