Diagonalizations of vector and tensor addition theorems

Bo He, W. C. Chew

Research output: Contribution to journalArticlepeer-review


Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula, an alternative and succinct derivation of the addition theorem for general tensor field is obtained. This new derivation facilitates the diagonalization of the tensor addition theorem. In order to complete this derivation, we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields. Since vector fields (special case of tensor fields) are very useful in practice, we discuss vector multipole fields and vector addition theorem in details. The work is important in multiple scattering and fast algorithms in wave physics.

Original languageEnglish (US)
Pages (from-to)797-819
Number of pages23
JournalCommunications in Computational Physics
Issue number4
StatePublished - Oct 2008


  • Addition theorem
  • Fast algorithm
  • Tensor field
  • Vector field

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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