Far-field approximations to the derivatives and integrals of the Green's function for the Ffowcs Williams and Hawkings equation

We report far-field approximations to the derivatives and integrals of the Green’s function for the Ffowcs Williams and Hawkings equation in the frequency domain. The approximations are based on the far-field asymptotic of the Green’s function. The details of the derivations of the proposed formulations are provided.