Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Translational addition theorems for prolate spheroidal vector wave functions $ {\bf M}^r$ and $ {\bf N}^r$


Authors: Jeannine Dalmas and Roger Deleuil
Journal: Quart. Appl. Math. 44 (1986), 213-222
MSC: Primary 33A55; Secondary 78A45
DOI: https://doi.org/10.1090/qam/856176
MathSciNet review: 856176
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Abstract: The translational addition theorems for prolate spheroidal vector wave functions $ {{\rm M}^r}$ and $ {{\rm N}^r}$ with reference to the spheroidal coordinate system at the origin 0 are obtained in terms of spheroidal vector wave functions with reference to the translated spheroidal coordinate system at the origin $ 0'$. These addition theorems are absolutely necessary for the study of the multiple scattering of electromagnetic waves when the single electromagnetic scattering solution is also expressed in terms of spheroidal vector wave functions $ {{\rm M}^r}$ and $ {{\rm N}^r}$.


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DOI: https://doi.org/10.1090/qam/856176
Article copyright: © Copyright 1986 American Mathematical Society

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