A version of Fabry’s theorem for power series with regularly varying coefficients

Eremenko, Alexandre

doi:10.1090/S0002-9939-08-09652-4

A version of Fabry’s theorem for power series with regularly varying coefficients
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by Alexandre Eremenko

Proc. Amer. Math. Soc. 136 (2008), 4389-4394

DOI: https://doi.org/10.1090/S0002-9939-08-09652-4

Published electronically: July 24, 2008

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Abstract:

For real power series whose non-zero coefficients satisfy $|a_m|^{1/m} \to ~1$, we prove a stronger version of Fabry’s theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.

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