Geodesic
On the transcendence and algebraic independence of the values of certain entire functions
Izvestiya. Mathematics, Tome 2 (1968) no. 1, pp. 61-87 
V. A. Oleinikov. On the transcendence and algebraic independence of the values of certain entire functions. Izvestiya. Mathematics, Tome 2 (1968) no. 1, pp. 61-87. http://geodesic.mathdoc.fr/item/IM2_1968_2_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we establish a criterion for the differential irreducibility of a general algebraic differential equation. We apply the results that are obtained to prove the transcendence and algebraic independence of the values at algebraic points of a collection of $E$-functions satisfying linear differential equations with polynomial coefficients.

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