Polynomial approximation of Maliuzhinets' function

Approximate formulas for the Maliuzhinets functions which give the solutions for the wedge diffraction with face impedance, are derived using the Chebyshev polynomials for various wedge angles. The coefficients of the polynomials are listed in a table. Although the formulas are derived for real variables, it is found that they can be used for the restricted range of complex variables. Since the validity of the formulas depends on both real and imaginary part when applied to complex variables, the equi-error contour of the formulas is given for the special case where the exact solution is available. An alternative but empirical formula for Maliuzhinets' functions is also obtained, which can be applied to arbitrary wedge angles.