Spheroidal Harmonic

A spheroidal harmonic is a special case of the Ellipsoidal Harmonic which satisfies the differential equation

$${d\over dx}\left[{(1-x^2){dS\over dx}}\right]+\left({\lambda-c^2x^2-{m^2\over 1-x^2}}\right)S=0$$

on the interval $-1\leq x\leq 1$.

See also Ellipsoidal Harmonic

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.