The asymptotic expansion of Green's function for the diffraction of short waves by a paraboloid of revolution (axisymmetric case)

Asymptotic expansions of Green's function are found which are equally valid in semi-shadow and shadow regions. Green's function is constructed for a paraboloid of revolution.
The stationary phase method is used in the illuminated region, and gives the formulae of geomerical acoustics. It enables the principal integration interval in the expressions for the currents on the surface of the paraboloid to be determined. In the semi-shadow and shadow regions Fok type expansions must be used.
Asymptotic expansions are found for the diffraction field in space.
The appendix discusses asymptotic expansions of Whittaker's degenerate function.