Rotational-translational addition theorems for scalar spheroidal wave functions

Authors:
R. H. MacPhie, J. Dalmas and R. Deleuil

Journal:
Quart. Appl. Math. **44** (1987), 737-749

MSC:
Primary 33A55

DOI:
https://doi.org/10.1090/qam/872824

MathSciNet review:
872824

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Abstract | References | Similar Articles | Additional Information

Abstract: Rotational-translational addition theorems for the scalar spheroidal wave function , with , are deduced. This permits one to represent the scalar spheroidal wave function, associated with one spheroidal coordinate system centered at its local origin , by an addition series of spheroidal wave functions associated with a second rotated and translated system , centered at . Such theorems are necessary in the rigorous analysis of radiation and scattering by spheroids with arbitrary spacings and orientations.

**[1]**B. Friedman and J. Russek,*Addition theorems for spherical waves*, Quart. Appl. Math.**12**, 13-23 (1954) MR**0060649****[2]**S. Stein,*Addition theorems for spherical wave functions*, Quart. Appl. Math.**19**, 15-24 (1961) MR**0120407****[3]**O. Cruzan,*Translational addition theorems for spherical vector wave functions*, Quart. Appl. Math.**20**, 33-40 (1962) MR**0132851****[4]**J. Bruning and Y. T. Lo,*Multiple scattering of EM waves by spheres, part I and part II*, IEEE Trans.**AP-19**, 378-400 (1971)**[5]**B. P. Sinha and R. H. MacPhie,*Translational addition theorems for spheroidal scalar and vector wave functions*, Quart. Appl. Math.**38**, 143-158 (1980) MR**580875****[6]**J. Dalmas and R. Deleuil,*Diffusion multiple des ondes électromagnétiques par des ellipsoïdes de révolution allongés*. Opt. Acta**29**, 1117-1131 (1982)**[7]**J. Dalmas and R. Deleuil,*Translational addition theorems for prolate spheroidal vector wave functions and*, Quart. Appl. Math.**44**, 213-222 (1986) MR**856176****[8]**B. P. Sinha and R. H. MacPhie,*Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids*, IEEE Trans.**AP-31**, 294-304 (1983)**[9]**J. Dalmas and R. Deleuil,*Multiple scattering of electromagnetic waves from two infinitely conducting prolate spheroids which are centered in a plane perpendicular to their axes of revolution*, Radio Sci.**20**, 575-581 (1985)**[10]**B. P. Sinha and R. H. MacPhie,*Mutual admittance characteristics for two-element parallel prolate spheroidal antenna systems*, IEEE Trans.**AP-33**, 1255-1263 (1985)**[11]**C. Flammer,*Spheroidal wave functions*, Stanford Univ. Press, Stanford, Calif. (1957) MR**0089520****[12]**A. R. Edmonds,*Angular momentum in quantum mechanics*, Princeton Univ. Press, Princeton, N. J. (1957) MR**0095700****[13]**J. A. Stratton,*Electromagnetic theory*, McGraw-Hill, New York (1941)**[14]**M. E. Rose,*Elementary theory of angular momentum*, Wiley, New York (1967)**[15]**D. M. Brink and G. R. Satchler,*Angular momentum*, Clarendon, Oxford (1962)**[16]**A. Erdelyi,*Higher transcendental functions*, McGraw-Hill, New York (1953)**[17]**M. Abramowitz and I. Stegun,*Handbook of mathematical functions*, Dover, New York (1965)**[18]**I. M. Gel'Fand and Z. Ya. Sapiro,*Representations of the group theory of rotations of a*3-*dimensional space and their applications*, Ann. Math. Soc. Transl., Ser. 2,**2**, 207-316 (1956) MR**0076290****[19]**S. L. Altmann and C. J. Bradley,*A note on the calculation of the matrix elements of the rotation group*, Philos. Trans. Roy. Soc. London, Ser. A,**255**, 193-198 (1963) MR**0148215**

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DOI:
https://doi.org/10.1090/qam/872824

Article copyright:
© Copyright 1987
American Mathematical Society