Fast evaluation of Gaunt coefficients: recursive approach

Solution of electromagnetic multisphere-scattering problems involves the determination of a large number of Gaunt coefficients that are connected with definite integrals of products of three associated Legendre functions. This paper presents general recursion formulae cycling a single index for the Gaunt coefficient. With the use of the recursive scheme, Gaunt coefficients of either low or high degree and order can be evaluated accurately and expeditiously.