General transformations between the Heun and Gauss hypergeometric functions

Details General transformations between the Heun and Gauss hypergeometric functions General transformations between the Heun and Gauss hypergeometric functions

2009-10-16

arxiv.org/abs/0910.3087v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

It is known that Heun's functions (or differential equations) can be reduced to Gauss hypergeometric functions by rational changes of its independent variable only if its parameters, including the fourth singular point location parameter and the accessory parameter, take special values. We present all hypergeometric-to-Heun transformations with two or three free continuous parameters up to fractional-linear transformations.

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