FAST EVALUATION OF THE GAUNT COEFFICIENTS

Addition theorems for vector spherical harmonics require the determina tion of the Gaunt coefficients that appear in a linearization expansio n of the product of two associated Legendre functions. This paper pres ents an algorithm for the efficient calculation of these coefficients through solving the most appropriate (lower triangular) linear system and derives all relevant recurrence relations needed in the calculatio n. This algorithm is also applicable to the calculation of the Clebsch -Gordan coefficients that are closely related to the Gaunt coefficient s and are frequently encountered in the quantum theory of angular mome ntum. The new method described in this paper reduces the computing tim e to similar to 1%, compared to the existing formulation that is widel y used. This new method can be applied to the calculation of both low- and high-degree coefficients, while the existing formulation works we ll only for low degrees.