Uniform asymptotic expansions of double integrals

Asymptotic Expansions for Integrals

Asymptotic Expansions of Symmetric Standard Elliptic Integrals

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...

Laplace Asymptotic Expansions for Gaussian Functional Integrals

We obtain a Laplace asymptotic expansion, in orders of λ, of Eρx { G(λx)e −2F (λx)} } the expectation being with respect to a Gaussian process. We extend a result of Pincus [9] and build upon the previous work of Davies and Truman [1, 2, 3, 4]. Our methods differ from those of Ellis and Rosen [6, 7, 8] in that we use the supremum norm to simplify the application of the result. A.M.S. Classifica...

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...

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...