ROTATIONAL‐TRANSLATIONAL ADDITION THEOREMS FOR VECTOR SPHEROIDAL WAVE FUNCTIONS

Abstract

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.

Citation

COORAY, M.F.R. and CIRIC, I.R. (1989), "ROTATIONAL‐TRANSLATIONAL ADDITION THEOREMS FOR VECTOR SPHEROIDAL WAVE FUNCTIONS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 8 No. 3, pp. 151-166. https://doi.org/10.1108/eb010056