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Asymptotic expansions for Taylor coefficients of the composition of two functions

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 item 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:Science > School of Mathematical, Physical and Computational 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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