Parametric Transformations between the Heun and Gauss Hypergeometric Functions

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概要

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• 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 P1 → P1. 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.

• 日本数学会函数方程式論分科会の論文

著者

• Filipuk Galina

  University of Warsaw

• Vidunas Raimundas

  National Kapodistrian University of Athens

関連論文

• Parametric Transformations between the Heun and Gauss Hypergeometric Functions

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