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arXiv · 0710.5894

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

Alexandre Eremenko
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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 theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.

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Alexandre Eremenko. 2008-04-22. A version of Fabry's theorem for power series with regularly varying coefficients. https://arxiv.org/abs/0710.5894

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