On the Algebraic Independence of the Values of Functions That Are Certain Integrals Involving the 1F1(1; λ + 1; z) Hypergeometric Function

Indefinite integrals of products of exponential functions, power functions and generalized hypergeometric functions of some types are considered. Necessary and sufficient conditions are established for the algebraic independence of large sets of such functions (for various parameters) and their derivatives, as well as their values. All the algebraic relations between these functions are written out explicitly.