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Computational Methods and Function Theory 1 (2001), No. 2, 433--455
Copyright Heldermann Verlag 2001

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences

Maria Teresa Alzugaray
mtrodrig@ualg.pt, A.D. de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Gambelas, 8000-117 Faro, Portugal.

[Abstract-pdf] [Abstract-ps]
We study the possible growth of Pólya frequency sequence generating functions 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.

Keywords: P\'olya frequency sequence, multiply positive sequence, generating function, proximate order, total positivity.

MSC 2000: 30B10, 30D99.

[FullText-pdf (244 K)] [FullText-ps (336 K)]