Efficient Ways to Compute the Vector Addition Theorem

Abstract

Two efficient ways of calculating the vector addition theorem are presented. One is obtained by relating the coefficients of the vector addition theorem to that of the scalar addition theorem for which an efficient recurrence relation exists. The second way is to derive recurrence relations directly for the coefficients of the vector addition theorem. These new ways of calculating the coefficients are of reduced computational complexity. Hence, when the number of coefficients required is large, the present methods are many times faster than the traditional method using Gaunt coefficients and Wigner 3j symbols.