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Now showing items 1-10 of 61

#### On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type

(Cambridge University Press, 2004)

We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. ...

#### Marginal states of the resistive tearing mode with flow in cylindrical geometry

(Cambridge University Press, 2004)

The linear stability of tearing modes in a cylindrical plasma subject to a sub-Alfvénic equilibrium shear flow along the equilibrium magnetic field is considered. The equations in the resistive boundary layer at the rational ...

#### Exactification of the method of steepest descents: the Bessel functions of large order and argument

(The Royal Society, 2004-09)

The Hadamard expansion procedure applied to Laplace–type integrals taken along contours in the complex plane enables an exact description of the method of steepest descents. This mode of expansion is illustrated by the ...

#### Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

(Elsevier, 2006-06)

We describe high-precision computations of the Pearcey integral Pe(x,y) for real x and y by means of Hadamard expansions. Numerical results for (x,y) situated in different regions of the x,y-plane are given to illustrate ...

#### Asymptotics and Mellin-Barnes integrals

(Cambridge University Press, 2001)

#### High-precision evaluation of the Bessel functions via Hadamard series

(Elsevier, 2009-02-01)

We present a method of high-precision calculation of the Bessel functions using Hadamard series. Such series are absolutely convergent expansions involving the normalised incomplete gamma function [formula missing] and ...

#### Exponentially small expansions in the asymptotics of the Wright function

(Elsevier, 2010-05)

We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest ...

#### The asymptotics of a new exponential sum

(Elsevier, 2009-01-01)

The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace ...

#### On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: real variable

(Elsevier, 2004-06)

We review and discuss the application of Hadamard expansions to the hyperasymptotic evaluation of Laplace integrals
where, for simplicity, in this paper x is restricted to be a positive real variable. The integration ...

#### The asymptotics of the generalised Hermite–Bell polynomials

(Elsevier, 2009-10-15)

The Hermite–Bell polynomials are defined by [formula missing] for n=0,1,2,… and integer r≥2 and generalise the classical Hermite polynomials corresponding to r=2. We obtain an asymptotic expansion for [formula missing] as ...