Transformations of some Gauss hypergeometric functions

Details Transformations of some Gauss hypergeometric functions Transformations of some Gauss hypergeometric functions

2003-10-28

arxiv.org/abs/math/0310436v2

J. Comp. Appl. Math., Vol. 178 (2005), pg. 473-487

Mathematics

Classical Analysis and ODEs

16 pages; the accepted text for publication (in the OPSFA 7 proceedings)

Scientific paper

This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences $1/K,1/L,1/M$ such that $K,L,M$ are positive integers and $1/K+1/L+1/M<1$. All algebraic transformations of these Gauss hypergeometric functions are considered. We show that apart from classical transformations of degree 2, 3, 4, 6 there are several other transformations of degree 6, 8, 9, 10, 12, 18, 24. Besides, we present an algorithm to compute relevant Belyi functions explicitly.

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