New algorithms for the computation of Malyuzhinets' special function

The paper presents new numerical techniques for computation of a special function introduced by G.D. Malyuzhinets to solve the canonical problem of diffraction of waves by a wedge with imperfectly reflecting (impedance) faces. Proposed schemes employ and combine various analytical representations of the function, including finite product, integral and large argument ones. In total, five numerical algorithms have been developed and implemented in FORTRAN subroutines differing from each other in accuracy and computational speed