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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - V. A. Gorelov
TI  - On the weakened Siegel's conjecture
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 33
EP  - 39
VL  - 11
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a4/
LA  - ru
ID  - FPM_2005_11_6_a4
ER  - 
%0 Journal Article
%A V. A. Gorelov
%T On the weakened Siegel's conjecture
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 33-39
%V 11
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a4/
%G ru
%F FPM_2005_11_6_a4
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/

[1] Galochkin A. I., “O kriterii prinadlezhnosti gipergeometricheskikh funktsii Zigelya klassu $E$-funktsii”, Mat. zametki, 29:1 (1981), 3–14 | MR | Zbl

[2] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Gostekhizdat, M., L., 1950

[3] Gorelov V. A., “Ob algebraicheskoi nezavisimosti znachenii $E$-funktsii v osobykh tochkakh i gipoteze Zigelya”, Mat. zametki, 67:2 (2000), 174–190 | MR | Zbl

[4] Gorelov V. A., “O gipoteze Zigelya dlya sluchaya lineinykh odnorodnykh differentsialnykh uravnenii 2-go poryadka”, Mat. zametki, 75:4 (2004), 549–565 | MR | Zbl

[5] Gorelov V. A., “O strukture mnozhestva $E$-funktsii, udovletvoryayuschikh lineinym differentsialnym uravneniyam 2-go poryadka”, Mat. zametki, 78:3 (2005), 331–348 | MR | Zbl

[6] Ditkin V. A., Prudnikov A. P., Integralnye preobrazovaniya i operatsionnoe ischislenie, FM, M., 1961

[7] Lyuk Yu., Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980

[8] Shidlovskii A. B., Transtsendentnye chisla, Nauka, M., 1987 | MR

[9] Andre Y., “Séries Gevrey de type arithmétique”, Ann. of Math., 151 (2000), 705–756 | DOI | MR