Geodesic
On the weakened Siegel's conjecture
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 33-39

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In the paper, we prove that two definitions of $E$-functions present in mathematics are equivalent if $E$-functions satisfy second-order linear differential equations. For this set of functions, a weakened variant of the well-known Siegel conjecture about representability of any $E$-function by a polynomial of hypergeometric functions is also proved. 
@article{FPM_2005_11_6_a4,
     author = {V. A. Gorelov},
     title = {On the weakened {Siegel's} conjecture},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {33--39},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a4/}
}
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V. A. Gorelov. On the weakened Siegel's conjecture. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 33-39. http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a4/