Series solution of a nonlocal dielectric test model for a solute ball with point charges in an ionic solvent

This paper reports an analytical solution of a nonlocal dielectric test model for a solute ball with multiple point charges in an ionic solvent. The solution is derived in a single sum series of Legendre polynomials and modified spherical Bessel functions so that it can be calculated efficiently for a large set of charges or a large set of mesh points. It also contains the series solution of a two-region Kirkwood ball model as a special case. This series solution can be valuable in the study of nonlocal dielectric continuum models and in the validation tests on the numerical algorithms and software packages for solving nonlocal Poisson-Boltzmann equation models.