Details:
Title  Transformations of some Gauss hypergeometric functions  Author(s)  Raimundas Vidūnas  Type  Article in Journal  Abstract  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.  Keywords  Gauss hypergeometric function, Algebraic transformation, Belyi function  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S0377042704004625 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  178  Number  1–2  Pages  473  487  Year  2005  Note  Proceedings of the Seventh International Symposium on Orthogonal Polynomials,Special Functions and Applications  Edition  0  Translation 
No  Refereed 
No 
