This article is cited in 1 paper

On algebraic properties of functions related to hypergeometric functions

V. A. Gorelov

National Research University "Moscow Power Engineering Institute"

Abstract: Functions given by indefinite integrals of products of elementary and generalized hypergeometric functions of some types are considered. Necessary and sufficient conditions for the algebraic independence of such functions and of their derivatives, as well as their values, are found. All the algebraic identities existing in these cases are found in closed form.

Keywords: generalized hypergeometric function, algebraic independence, Siegel's method, $E$-function.

UDC: 511.36

Received: 25.02.2024

DOI: 10.4213/mzm14293

 English version: Mathematical Notes, 2025, 117:3, 383–391

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