A version of Fabry's theorem for power series with regularly varying coefficients
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🧮 math.CV
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coefficientspowerseriesfabrytheoremversionanalyticchanges
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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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