Diagonalizations of Vector and Tensor Addition Theorems (Communications in Computational Physics, 2008)
Based on the generalizations of the Funk-Hecke formula and the Rayleighplan-wave expansion formula, an alternative and succinct derivation of the additiontheorem for general tensor field is obtained. This new derivation facilitates the diagonalization of the tensor addition theorem. In order to complete this derivation, wehave carried out the evaluation of the generalization of the Gaunt coefficient for tensorfields. Since vector fields (special case of tensor fields) are very useful in practice, wediscuss vector multipole fields and vector addition theorem in details. The work isimportant in multiple scattering and fast algorithms in wave physics.