Mixed powers of generating functions
| dc.creator | Lladser, Manuel | |
| dc.date | 2006-08-15 | |
| dc.date.accessioned | 2026-07-07T08:08:06Z | |
| dc.date.available | 2026-07-07T08:08:06Z | |
| dc.description | Given an integer m>=1, let || || be a norm in R^{m+1} and let S denote the set of points with nonnegative coordinates in the unit sphere with respect to this norm. Consider for each 1<= j<= m a function f_j(z) that is analytic in an open neighborhood of the point z=0 in the complex plane and with possibly negative Taylor coefficients. Given a vector n=(n_0,...,n_m) with nonnegative integer coefficients, we develop a method to systematically associate a parameter-varying integral to study the asymptotic behavior of the coefficient of z^{n_0} of the Taylor series of (f_1(z))^{n_1}...(f_m(z))^{n_m}, as ||n|| tends to infinity. The associated parameter-varying integral has a phase term with well specified properties that make the asymptotic analysis of the integral amenable to saddle-point methods: for many directions d in S, these methods ensure uniform asymptotic expansions for the Taylor coefficient of z^{n_0} of (f_1(z))^{n_1}...(f_m(z))^{n_m}, provided that n/||n|| stays sufficiently close to d as ||n|| blows up to infinity. Our method finds applications in studying the asymptotic behavior of the coefficients of a certain multivariable generating functions as well as in problems related to the Lagrange inversion formula for instance in the context random planar maps. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608398 | |
| dc.identifier | http://arxiv.org/abs/math/0608398 | |
| dc.identifier | Discrete Mathematics and Theoretical Computer Science Proceedings, AG, 171-182, 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131150 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 05A15, 05A16, 30B10, 41A60, 60C05 | |
| dc.title | Mixed powers of generating functions | |
| dc.type | text |