Geodesic
Algebraic Relations between the Hypergeometric E-Function and Its Derivatives
Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 832-844 
V. Kh. Salikhov; G. G. Viskina. Algebraic Relations between the Hypergeometric E-Function and Its Derivatives. Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 832-844. http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a3/
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     title = {Algebraic {Relations} between the {Hypergeometric} {E-Function} and {Its} {Derivatives}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the generalized hypergeometric function $$ \sum _{n=0}^\infty \frac 1{(\lambda _1+1)_n\dotsb(\lambda _t+1)_n} \biggl (\frac zt\biggr )^{tn}, \qquad\lambda _1,\dots,\lambda _t\in\mathbb Q\setminus\{-1,-2,\dots\}, $$ where $t$ is an even number, and its derivatives up to the order $t- 1$ inclusive. In the case of algebraic dependence between these functions over $\mathbb C(z)$, a complete structure of algebraic relations between them is given.

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