The asymptotic expansion of Gordeyev's integral
type: Item
instance of: scholarly article
title: The asymptotic expansion of Gordeyev's integral
zbMATH Open document ID: 0905.41019
DOI: 10.1007/PL00001486
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1999-01-11T00:00:00Z
review text: The integral reads \(G_\nu(\omega, \lambda)=\omega\int_0^\infty \exp[i\omega t-\lambda(1-\cos t)-{1\over 2}\nu t^2] dt\), with \(\text{Re}(\nu)>0\). This integral occurs in the study of the propagation of electrostatic waves in a hot magnetised Maxwellian plasma. The steepest descent method is used to obtain an asymptotic expansion for large values of \(\omega\) and \(\lambda\) and \(\nu \to 0^+\). The expansions are compared with numerically computed values of the integral.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 78A40
Mathematics Subject Classification ID: 76X05
zbMATH DE Number: 1151831
zbMATH Keywords: Gordeyev's integral
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: steepest descent
zbMATH Keywords: Stokes phenomenon
author: Richard B. Paris
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: pl00001486
OpenAlex ID: W4250985901
description: scientific article; zbMATH DE number 1151831