On $PC$-ansatz

The subject of the paper is detailed consideration of known from seventies ansatz:
$$ e^{\operatorname{i}kl(x)}[AD_p(\sqrt{k}e^{-\frac\pi4}m(x))+ k^{-\frac12}e^{\frac\pi4}BD_p^\prime(\sqrt{k}e^{-\frac\pi4}m(x))], $$
where $A$ and $B$ are series:
$$ A=\sum_{s=0}^\infty\frac{A_s(x)}{(\operatorname{i}k)^s};\quad B=\sum_{s=0}^\infty\frac{B_s(x)}{(\operatorname{i}k)^s}. $$
Here $D_p$ are parabolic cylinder functions. Analytical expressions in the first approximation for wave field in the penumbra of the wave reflected by impedance or transparent cone were obtained.