The first solution to Lamé's Differential Equation, denoted for ,
..., . They are also called Lamé Functions. The product of two ellipsoidal harmonics of
the first kind is a Spherical Harmonic. Whittaker and Watson (1990, pp. 536-537) write

(1) | |||

(2) |

and give various types of ellipsoidal harmonics and their highest degree terms as

- 1.
- 2.
- 3.
- 4. .

(3) |

(4) |

Byerly (1959) uses the Recurrence Relations to explicitly compute some ellipsoidal harmonics, which he denotes by , , , and ,

**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, pp. 254-258, 1959.

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

© 1996-9

1999-05-25