  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.

Classical Analysis and ODEs