An exact and asymptotic analysis of a diffraction problem

The present analysis deals with diffraction of acoustic waves by an oscillating strip focusing on the exact and concise formulation of a series solution in the complex domain. The complete solution is represented by a series, the eigenfunctions of which are generalized gamma functions. An exact expression of this special function, with argument being 'integer +1/2', is derived. The convergence analysis of the series solution in transformed domain is discussed graphically. Finally, the scattered and total acoustic fields are obtained by exact and asymptotic evaluations of inverse Fourier transforms. The significance of the present investigation is the derivation of a high order accurate solution in a convenient form.