Computation of the Multi-Spheres Scattering Coefficient by Prime-Index Method

The analytical-numerical evaluation of the scattering of electromagnetic waves by multiple spheres requires the computation of numerous coefficients. For this purpose, many contributions, available in the literature, have traditionally employed the recursion method. In the present paper, we introduce a novel approach, based on primes and indices, which can be conveniently applied to the computation of the Wigner 3-j symbols, the Wigner D-function, and the Gaunt coefficients. By considering a series-expansion form, our method proves to be easily applicable to a variety of similar problems. We provide examples of coefficient calculations and compare the results with those retrieved from previous publications, demonstrating the advantages of our approach.