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Article type: Research Article
Authors: Hilberdink, Titus
Affiliations: Department of Mathematics, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, England, UK. E-mail: t.w.hilberdink@reading.ac.uk
Abstract: We give an asymptotic expansion for the Taylor coefficients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coefficients vary ‘smoothly’ and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.
Keywords: asymptotic expansions, Taylor coefficients, weighted renewal sequences
DOI: 10.3233/ASY-2008-0926
Journal: Asymptotic Analysis, vol. 63, no. 3, pp. 125-142, 2009
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