On the proximate order of growth of generating functions of Polya frequency sequences

Maria Teresa Alzugaray

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On the proximate order of growth of generating functions of Polya frequency sequences

Maria Teresa Alzugaray

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Abstract

We study the possible growth of $PF_r$ g.f.'s analytic in the unit disk and describe the proximate orders of growth of these functions. Some classical function theory results concerning orders of growth are generalized to the case of proximate orders.

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Maria Teresa Alzugaray. 2002-10-28. On the proximate order of growth of generating functions of Polya frequency sequences. https://arxiv.org/abs/math/0210429

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