On the Siegel Conjecture for Second-Order Homogeneous Linear Differential Equations
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 549-565.

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The structure of the set of $E$-functions satisfying second-order homogeneous linear differential equations with coefficients from ${\mathbb C} (z)$ is described.
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V. A. Gorelov. On the Siegel Conjecture for Second-Order Homogeneous Linear Differential Equations. Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 549-565. http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a4/

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

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

[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] Krattser A., Frants V., Transtsendentnye funktsii, IL, M., 1963

[5] Shidlovskii A. B., “O transtsendentnosti znachenii $E$-funktsii, yavlyayuschikhsya resheniyami lineinykh differentsialnykh uravnenii vtorogo poryadka”, Matem. sb., 184:5 (1993), 75–84

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

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

[8] Strelits Sh. I., “O roste reshenii lineinykh differentsialnykh uravnenii vtorogo poryadka”, Matem. sb., 46:4 (1958), 433–450 | MR | Zbl

[9] Vittikh G., Noveishie issledovaniya po odnoznachnym analiticheskim funktsiyam, FM, M., 1960

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

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