On power series whose tails have multiply positive coefficients

Natalya Zheltukhina

Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey

Abstract: Entire functions whose tails have $4$-times positive coefficients are studied. The growth estimate for such functions is given. It is shown that the same growth estimate holds for entire functions of order $<1$ whose tails do not have zeros in the angle $\{z:|{\arg z}|\leq 4\pi /5\}$.

MSC: 30B10, 30D15

Received: 03.08.2002

Language: English

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