Geodesic
On a convergence of formal power series under a special condition on the Gelfond–Leont'ev derivatives
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 2, pp. 241-252 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a formal power series the conditions on the Gelfond–Leont'ev derivatives are found, under which the series represents a function, analytic in the disk $\{z:|z|, $0. 
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M. M. Sheremeta; O. A. Volokh. On a convergence of formal power series under a special condition on the Gelfond–Leont'ev derivatives. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 2, pp. 241-252. http://geodesic.mathdoc.fr/item/JMAG_2007_3_2_a6/

[1] A. O. Gelfond, A. F. Leont'ev, “On a Generalisation of Fourier Series”, Mat. Sb., 29:3 (1951), 477–500 (Russian) | MR | Zbl

[2] M. M. Sheremeta, “On Power Series with Gelfond–Leont'ev Derivatives Satisfying a Special Condition”, Mat. phys., anal., geom., 3 (1996), 423–445 (Russian) | MR | Zbl

[3] O. A. Volokh, M. M. Sheremeta, “On Formal Power Series with Gelfond–Leont'ev Derivatives Satisfying a Special Condition”, Mat. Stud., 22:1 (2004), 87–93 (Ukraine) | MR | Zbl