MR3114824
Raimundas VIDUNAS and Galina FILIPUK
Raimundas VIDUNAS and Galina FILIPUK
Parametric Transformations between the Heun and Gauss Hypergeometric Functions
Funkcialaj Ekvacioj. Serio Internacia
56
2013
271--321
http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-2/56_271.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3114824
The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings $\mathbb{P}^1\to\mathbb{P}^1$. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the list of hypergeometric-to-Heun pull-back transformations with a free continuous parameter, and illustrates most of them by a Heun-to-hypergeometric reduction formula. In total, 61 parametric transformations exist, of maximal degree 12.
Heun equation, Hypergeometric equation, Heun function, Gauss hypergeometric function.
Primary 33E30, Secondary 33C05.
56-271
2013
Parametric Transformations between the Heun and Gauss Hypergeometric Functions
Raimundas VIDUNAS and Galina FILIPUK
Raimundas VIDUNAS and Galina FILIPUK
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