Helmholtz Differential Equation--Prolate Spheroidal Coordinates

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz Differential Equation is separable in Prolate Spheroidal Coordinates.

References

Arfken, G. ``Prolate Spheroidal Coordinates $(u, v, \varphi)$.'' §2.10 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 103-107, 1970.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 661, 1953.