Addition theorems for electromagnetic wave scattering by spheroids of arbitrary orientation

Rotational-translation addition theorems for two vector spheroidal wave functions are derived from those for the corresponding scalar spheroidal wave functions. These theorems are necessary in obtaining an exact eigenfunction to the problem of scattering of electromagnetic waves by a system of two or more spheroids of arbitrary orientations. A vector spheroidal wave function defined on one spheroidal coordinate system is expressed in terms of a series of vector spheroidal wave functions in another spheroidal coordinate system rotated and translated with respect to the first one. The theorems presented represent an extension of the rational-translational addition theorems for scalar wave functions. Corresponding translational addition theorems for vector spheroidal wave functions of R.H. MacPhie et al. (see Quart. Appl. Math., vol.44, p.737, 1987) result as a special case.<>