Algebraicity of the Appell-Lauricella and Horn hypergeometric functions

Abstract

We extend Schwarz' list of irreducible algebraic Gauss functions to the four classes of Appell-Lauricella functions in several variables and the 14 complete Horn functions in two variables. This gives an example of a family of functions such that for any number of variables there are infinitely many algebraic functions, namely the Lauricella $F_C$ functions.

arXiv comment24 pages, 6 tables, 2 figures