## Lamé's Differential Equation

 (1)

(Byerly 1959, p. 255). The solution is denoted and is known as a Lamé Function or an Ellipsoidal Harmonic. Whittaker and Watson (1990, pp. 554-555) give the alternative forms
 (2)

 (3)

 (4)

 (5)

where is a Weierstraß Elliptic Function and
 (6) (7) (8)

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, 1959.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.