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Asymptotic expansions for Taylor coefficients of the composition of two functions

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Hilberdink, T. (2009) Asymptotic expansions for Taylor coefficients of the composition of two functions. Asymptotic Analysis, 63 (3). pp. 125-142. ISSN 1875-8576

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To link to this article DOI: 10.3233/ASY-2008-0926

Abstract/Summary

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:23294
Uncontrolled Keywords:asymptotic expansions; Taylor coefficients; weighted renewal sequences
Publisher:IOS Press
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