Excitation coefficients of the whispering gallery waves in a vicinity of concave boundary with curvature vanishing at a point

A method is presented for computing the excitation coefficients of whispering gallery waves arising behind a given point, at which the curvature of the concave boundary vanishes. Absolute values of some coefficients for the incident whispering gallery waves № 1 and № 2 are computed. It follows from these results that the principal part of the incident wave energy in both cases is transformed into the whispering gallery wave № 1.