Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Translational addition theorems for spheroidal scalar and vector wave functions


Authors: Bateshwar P. Sinha and Robert H. Macphie
Journal: Quart. Appl. Math. 38 (1980), 143-158
MSC: Primary 33A55
DOI: https://doi.org/10.1090/qam/580875
MathSciNet review: 580875
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Abstract: The translational addition theorems for spheroidal scalar wave functions $ R_{mn}^{\left( i \right)}\left( {h, \xi } \right){S_{mn}}\left( {h, \eta } \right)\exp \left( {jm\phi } \right); i = 1, 3, 4$ and spheroidal vector wave functions $ M_{mn}^{x, y, z\left( i \right)}\left( {h; \xi , \\ \eta, \phi } \right), N_{mn}^{x, y, z\left( i \right)}\left( {h; \xi, \eta, \phi } \right); i = 1, 3, 4$, with reference to the spheroidal coordinate system at the origin $ O$, have been obtained in terms of spheroidal scalar and vector wave functions with reference to the translated spheroidal coordinate system at the origin $ O'$, where $ O'$ has the spherical coordinates ( $ {r_0},{\theta _0},{\phi _0}$) with respect to $ O$. These addition theorems are useful in acoustics and electromagnetics in those cases involving spheroidal radiators and scatterers.


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DOI: https://doi.org/10.1090/qam/580875
Article copyright: © Copyright 1980 American Mathematical Society


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