Rotational-translational addition theorems for vector spheroidal wave functions

• M.F.R. Cooray ^[1] ; I.R. Ciric ^[1]
  1. [1] University of Manitoba

     University of Manitoba

     Canadá

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 8, Nº 3, 1989, págs. 151-166
• Idioma: inglés
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• Resumen

  • Rotational‐translational addition theorems for the vector spheroidal wave functions Ma(i)mn(h; ξ, η, φ) and Na(i)mn(h; ξ, η, φ), i = 1,2,3,4, are derived from those for the corresponding scalar spheroidal wave functions ψ(i)mn(h; ξ, η, φ). A vector spheroidal wave function defined in one spheroidal coordinate system (h; ξ, η, φ) is expressed in terms of a series of vector spheroidal wave functions defined in another spheroidal coordinate system (h′; ξ′, η′, φ′), which is rotated and translated with respect to the first one. These theorems allow a rigorous treatment of boundary value problems relative to time‐harmonic vector field waves in the presence of a system of spheroids with arbitrary orientations. As a special case, general rotational‐translational addition theorems for vector spherical wave functions are also presented.