Spherical Harmonic Differential Equation

In three dimensions, the spherical harmonic differential equation is given by

and solutions are called spherical harmonics (Zwillinger 1997, p. 130). In four dimensions, the spherical harmonic differential equation is

(Humi 1987; Zwillinger 1997, p. 130).

REFERENCES:

Humi, M. "Factorisation of Separable Partial Differential Equations." J. Phys. A: Math. Gen. 20, 4577-4585, 1987.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 130, 1997.