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Surface Harmonic


Any linear combination of real spherical harmonics

 A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta)

for l fixed whose sum is not premultiplied by a factor r^l (Whittaker and Watson 1990, p. 392).


See also

Solid Harmonic, Spherical Harmonic

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References

Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, p. 197, 1959.Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

Referenced on Wolfram|Alpha

Surface Harmonic

Cite this as:

Weisstein, Eric W. "Surface Harmonic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SurfaceHarmonic.html

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