Accurate Efficient Evaluation of Lommel Functions for Arbitrarily Large Arguments
Eric L. Shirley, E K. Chang
It can be difficult to evaluate Lommel functions U_n(u,v) and V_n(u,v) when u and v are both large. Here, we present an accurate means to evaluate such functions using contour integration. The approach suggests the potential for developing analogous techniques in diffraction calculations for many optical systems.