Closed-form expression of the Maliuzhinets function using tanh-sinh quadrature rule

The Maliuzhinets function (MF) has been used for the diffraction problem of waves by a wedge with different face impedances. For a wedge with arbitrary angle, the Maliuzhinets function is cumbersome to compute which is a major limitation to the use of rigorous theory of diffraction in electromagnetic scattering by a wedge with impedance faces. In this work, an exact closed-form solution is obtained to evaluate a known integral representation of the MF. The tanh - sinh quadrature rule is employed to successfully calculate the integral in the Maliuzhinets function, and the highly accurate numerical computation for Ψ_n(z) is obtained over the entire complex z plane and for all n. For special wedge angles, the exact formulation is numerically verified by comparing it with the results obtained by numerical integration of the Maliuzhinets function.