Spherical Harmonic Addition Theorem
المؤلف:
Arfken, G.
المصدر:
"The Addition Theorem for Spherical Harmonics." §12.8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press
الجزء والصفحة:
pp. 693-695
24-9-2019
2714
Spherical Harmonic Addition Theorem
A formula also known as the Legendre addition theorem which is derived by finding Green's functions for the spherical harmonic expansion and equating them to the generating function for Legendre polynomials. When 
is defined by
 |
(1)
|
The Legendre polynomial of argument 
is given by
Another version of the formula can be given as
 |
(5)
|
(O. Marichev, pers. comm., Jan. 15, 2008).
REFERENCES:
Arfken, G. "The Addition Theorem for Spherical Harmonics." §12.8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 693-695, 1985.
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