Recurrence relations for the elements of a translation matrix in the scalar addition theorem in three-dimensions using spherical harmonics are derived. These recurrence relations are more efficient to evaluate compared to the use of Gaunt coefficients evaluated with Wigner 3j symbols or with recurrence relations. The efficient evaluation of the addition theorem is important in a number of wave scattering calculations including fast recursive algorithms.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Electrical and Electronic Engineering