Transformation to canonical form for uniform asymptotic expansions

Uniform Asymptotic Expansions for Charlier Polynomials

The asymptotic behaviour of the Charlier polynomials C (a) n (x) as nQ. is examined. These polynomials satisfy a discrete orthogonality relation and, unlike classical orthogonal polynomials, do not satisfy a second-order linear differential equation with respect to the independent variable x. As such, previous results on their asymptotic behaviour have been restricted to integral methods and co...

Uniform Asymptotic Expansions of Multiple Scattering Iterations

Although every implementation of a recent high frequency multiple scattering solver has displayed a frequency independent operation count, its numerical analysis yet remains as a challenging open problem. This is, in part, due to the absence of detailed information on the uniform asymptotic expansions of multiple scattering iterations. Here we address precisely this issue for a collection of co...

Zero bias transformation and asymptotic expansions

We apply the zero bias transformation to deduce a recursive asymptotic expansion formula for expectation of functions of sum of independent random variables in terms of normal expectations and we discuss the remainder term estimations. MSC 2000 subject classifications: 60G50, 60F05.

Asymptotic Expansions for Integrals

Zero bias transformation and asymptotic expansions II : the Poisson case

We apply a discrete version of the methodology in [12] to obtain a recursive asymptotic expansion for E[h(W )] in terms of Poisson expectations, where W is a sum of independent integer-valued random variables and h is a polynomially growing function. We also discuss the remainder estimations. MSC 2000 subject classifications: 60G50, 60F05.