Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Translational addition theorems for spherical vector wave functions


Author: Orval R. Cruzan
Journal: Quart. Appl. Math. 20 (1962), 33-40
MSC: Primary 33.28
DOI: https://doi.org/10.1090/qam/132851
MathSciNet review: 132851
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Abstract: Translational addition theorems for spherical vector wave functions have been derived in a reduced form. The reduction has been accomplished by the use of formulas relating the coefficients that arise in the expansion of the product of two associated Legendre functions. These addition theorems should be useful, in general, in those cases involving electromagnetic sources and spherical bodies.


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  • [1] S. Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19, 15-24 (1961) MR 0120407
  • [2] S. Stein, Addition theorems for spherical wave functions, Hermes Electronics Co., Cambridge, Mass., Tech. Rept. No. 1 under Nonr-2632(00), Hermes Electronics Rept. M-697, 15 August 1959 MR 0120407
  • [3] S. Stein, Ibid., p. 33
  • [4] O. R. Cruzan, Translational addition theorems for spherical vector wave functions, Diamond Ordnance Fuze Labs., Washington 25, D. C., Tech. Rept. TR-906, 10 March 1961 MR 0132851
  • [5] J. A. Stratton, Electromagnetic theory, McGraw-Hill Book Co., Inc., New York, N. Y., 1941, pp. 392-423
  • [6] A. R. Edmonds, Angular momentum in quantum mechanics, Princeton Univ. Press, Princeton, N. J., 1957 MR 0095700
  • [7] B. Friedman and J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12, 13-23 (1954) MR 0060649

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DOI: https://doi.org/10.1090/qam/132851
Article copyright: © Copyright 1962 American Mathematical Society

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