Uniform Airy-Type Expansions of Integrals

Symbolic Evaluation of Coefficients in Airy-type Asymptotic Expansions

Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function. 1991 Mathematics Subject Classification: 41A60, 33C10, 33C15, 33F05, 65D20.

Asymptotic Expansions for Integrals

Two-point Taylor Expansions of Analytic Functions

In deriving uniform asymptotic expansions of a certain class of integrals one encounters the problem of expanding a function, that is analytic in some domain Ω of the complex plane, in two points. The first mention of the use of such expansions in asymptotics is given in [1], where Airy-type expansions are derived for integrals having two nearby (or coalescing) saddle points. This reference doe...

Modelling, Analysis and Simulation Symbolic evaluation of coefficients in Airy-type asymptotic expansions

Computer algebra algorithms are developed for evaluating the oeÆ ients in Airy-type asymptoti expansions that are obtained from integrals with a large parameter. The oeÆ ients are de ned from re ursive s hemes obtained from integration by parts. An appli ation is given for the Weber paraboli ylinder fun tion. 2000 Mathemati s Subje t Classi ation: 41A60, 33C10, 33C15, 33F05, 65D20.

Gevrey expansions of hypergeometric integrals I

We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains are one dimensional. We prove that any Gevrey series solution along the singular support of the system is the asymptotic expansion of a holomorphic solution given by a carefully...