Asymptotische Darstellung verallgemeinerter Fourierintegrale IV

Abstract

The asymptotic behavior of Fourier integrals of the form

where the parameter $s$ tends to a critical point $s_0$, is considered. It is provided that $H(i,s)$ has at $t=a$ a stationary point of (fractional) order $\beta >0$, and the Fourier transform of the function $K(\tau )$ is given in closed form. Under certain conditions it is demonstrated that it’s possible to obtain an asymptotical expansion of this integral by the Fourier transform of the function $K$.