Geodesic
On the Structure of the Set of $E$-Functions Satisfying Linear Differential Equations of Second Order
Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 331-348 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a special case of Siegel's conjecture concerning the representability of $E$-functions in the form of polynomials in hypergeometric functions. We prove several assertions (formulated earlier by A. B. Shidlovskii) about the transcendence and linear independence of values of $E$-functions. 
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V. A. Gorelov. On the Structure of the Set of $E$-Functions Satisfying Linear Differential Equations of Second Order. Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 331-348. http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a1/

[1] Siegel C. L., “Über einige Anwendungen diophantischer Approximationen”, Abh. Preuss. Acad. Wiss. Phys.-Math. Kl., 1929–1930, no. 1, 1–70

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

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

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

[5] Shidlovskii A. B., “O lineinoi nezavisimosti znachenii $E$-funktsii v algebraicheskikh tochkakh”, Matem. zametki, 55:2 (1994), 174–185 | MR

[6] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971 | MR

[7] Ains E. L., Obyknovennye differentsialnye uravneniya, Kharkov, 1939

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

[9] Perron O., “Über lineare Differentialgleichungen mit rationalen Koeffizienten”, Acta Math., 34 (1911), 139–163 | DOI

[10] Valiron Zh., Analiticheskie funktsii, Gostekhizdat, M., 1957