Fast and accurate Fourier series solutions to gravitational lensing by a general family of two power-law mass distributions

Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two power-law ellipsoidal mass distributions are presented. The cusped two power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e. g., 10(-5)). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single power-law mass model are made publicly available.