Whittaker and Weyl representations for time-domain modes

In the spectral theory of transients one may express the temporal wavefield inside a waveguide in terms of an angular integral representation of global time-domain spectral-mode constituents. The remaining spectral integral may be evaluated asymptotically. Depending of the choice of the large parameter, the evaluation of the integrals along steepest descent paths yields Whittaker- or Weyl expansions for time-domain modes.