On generating function of Weber parabolic cylinder functions with a negative integer index and radio pulse deformation by a medium

A generating function for parabolic cylinder functions with a negative integer index is considered. The generating function is expressed as a contour integral depending on two complex variables. Asymptotic expressions are obtained, and value tables of this integral are given. Its role in the problem concerning one-dimensional propagation of an electromagnetic field is noted. The EM field was originally a radio pulse with the Gaussian envelope in the medium with anomalous dispersion.