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

Mathematics – Complex Variables

Scientific paper

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26 pages, to appear in Computational Methods and Function Theory

Scientific paper

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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