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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/23294
Identification Number/DOI	10.3233/ASY-2008-0926
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	asymptotic expansions; Taylor coefficients; weighted renewal sequences
Publisher	IOS Press
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