On power serieshaving sectionswith multiply positive coefficients

Date

2002-03-15

Authors

Zheltukhina, N. A.

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Abstract

Polya’s theorem of 1913 says that if all sections of power series have real negative zeros only, then the series converges in the whole complex plane and its sum satisfies a certain growth condition. Here we show that the assertion of Po´ lya’s theorem remains valid for a much larger class of formal power series and, moreover, a better growth estimate holds.

Source Title

Complex Variables

Publisher

Taylor & Francis

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Published Version (Please cite this version)

Language

English