Geodesic
On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations
Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 587-598

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We prove a theorem which reduces the investigation of the algebraic independence of solutions of linear nonhomogeneous systems of differential equations to the investigation of homogeneous systems. We use this theorem to prove the algebraic independence of the values of certain $E$-functions. 
@article{MZM_1969_5_5_a11,
     author = {Yu. V. Nesterenko},
     title = {On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {587--598},
     publisher = {mathdoc},
     volume = {5},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a11/}
}
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Yu. V. Nesterenko. On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations. Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 587-598. http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a11/