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