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Spheroidal Harmonic


A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation

 d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0

on the interval -1<=x<=1.


See also

Ellipsoidal Harmonic of the First Kind, Ellipsoidal Harmonic of the Second Kind, Spheroidal Wave Function

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "A Worked Example: Spheroidal Harmonics." §17.4 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 764-773, 1992.

Referenced on Wolfram|Alpha

Spheroidal Harmonic

Cite this as:

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

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