On Algebraic Independence of Solutions of Generalized Hypergeometric Equations

Abstract

We present solutions for general theorems regarding algebraic independence of solutions of hypergeometric equation ensembles and the values of these solutions at algebraic points. The conditions of the theorems are necessary and sufficient. Furthermore, errors in theorems from F. Beukers and others are corrected.

Keywords

• generalized hypergeometric functions
• algebraic independence
• Siegel’s method