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

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

2007-10-31

arxiv.org/abs/0710.5894v2

PAMS, 136 (2008), 4389-4394

Mathematics

Complex Variables

7 pages

Scientific paper

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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