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arXiv · 0910.3087

Parametric transformations between the Heun and Gauss hypergeometric functions

Raimundas Vidunas·Galina Filipuk
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Abstract

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-to-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.

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Raimundas Vidunas, Galina Filipuk. 2012-04-27. Parametric transformations between the Heun and Gauss hypergeometric functions. https://doi.org/10.1619/fesi.56.271

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