On the Algebraic Independence of the Values of Functions Associated with Hypergeometric Functions

Abstract

Functions that are integrals of products of generalized hypergeometric functions of some kind are considered. The conditions for the representability of these functions as a polynomial in hypergeometric ones are found. The necessary and sufficient conditions for the algebraic independence of such functions are established.

Keywords

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