Asymptotics at irregular singular points

The Stokes Phenomenon in Exact Asymptotics

As an introduction we present a new, elementary and constructive proof of the multisummability properties of formal solutions of linear ODE’s at irregular singular points. This serves to illustrate the geometric approach to multisummation. Basic properties of multisums and the associated sheaves are derived. Next, we study Cauchy-Heine transforms in relation to multisummation and the Stokes phe...

Asymptotics of Multivariate Sequences, Part I: Smooth Points of the Singular Variety

Given a multivariate generating function F (z1, . . . , zd) = ∑ ar1,... ,rdz r1 1 · · · z rd d , we determine asymptotics for the coefficients. Our approach is to use Cauchy’s integral formula near singular points of F , resulting in a tractable oscillating integral. This paper treats the case where the singular point of F is a smooth point of a surface of poles. Companion papers will treat sin...

Asymptotics of Multivariate Sequences , Part I : Smooth Points Ofthe Singular

Gevrey Solutions of the Irregular Hypergeometric System Associated with an Affine Monomial Curve

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.

A Discrete Singular Convolution Method for the Seepage Analysis in Porous Media with Irregular Geometry

A novel discrete singular convolution (DSC)  formulation  is  presented for the seepage analysis in irregular geometric porous media. The DSC is a new promising numerical approach which has been recently applied to solve several engineering problems. For a medium with regular geometry, realizing of the DSC for the seepage analysis is straight forward. But DSC implementation for a medium with ir...