The asymptotic expansion of Gordeyev's integral
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.
scientific article; zbMATH DE number 1151831