This article is cited in 7 papers

On the Structure of the Set of $E$-Functions Satisfying Linear Differential Equations of Second Order

V. A. Gorelov

Moscow Power Engineering Institute (Technical University)

Abstract: We prove a special case of Siegel's conjecture concerning the representability of $E$-functions in the form of polynomials in hypergeometric functions. We prove several assertions (formulated earlier by A. B. Shidlovskii) about the transcendence and linear independence of values of $E$-functions.

UDC: 511.36

Received: 03.06.2004

DOI: 10.4213/mzm2591

 English version: Mathematical Notes, 2005, 78:3, 304–319

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