Parametric Transformations between the Heun and Gauss Hypergeometric Functions

DOI10.1619/fesi.56.271zbMath1279.33030arXiv0910.3087OpenAlexW3104856548MaRDI QIDQ2868895

Galina Filipuk, Raimundas Vidunas

Publication date: 19 December 2013

Published in: Funkcialaj Ekvacioj (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.3087

zbMATH Keywords

Gauss hypergeometric functionHeun equationhypergeometric equationHeun function

Mathematics Subject Classification ID

Other functions coming from differential, difference and integral equations (33E30) Classical hypergeometric functions, ({}_2F_1) (33C05)

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The third five-parametric hypergeometric quantum-mechanical potential ⋮ Classifying (almost)-Belyi maps with five exceptional points ⋮ Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Appell hypergeometric expansions of the solutions of the general Heun equation ⋮ Heun functions and diagonals of rational functions ⋮ Heun equations coming from geometry ⋮ Generalized hypergeometric solutions of the Heun equation ⋮ On the derivatives of the Heun functions ⋮ A classification of coverings yielding Heun-to-hypergeometric reductions ⋮ Belyi functions for hyperbolic hypergeometric-to-Heun transformations ⋮ On metrics of curvature 1 with four conic singularities on tori and on the sphere ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

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