Lamé Functions

Lamé functions

[lä′mā ‚fəŋk·shənz]
Functions that arise when Laplace's equation is separated in ellipsoidal coordinates.

Lamé Functions


functions used in studying physical phenomena (distribution of heat, the motion of a fluid) in regions bounded by the surface of an ellipsoid. Lamé functions L(λ) are the simplest solutions of the Lamé differential equation

where a2 = a2+ λ, β2 = b2+ λ, y2 = c2+ λ, n is an integer, and a, b, and c are the semiaxes of the ellipsoid inside (or outside) of which the physical phenomenon is to be studied. Lamé functions, introduced by G. Lamé in 1839, find many applications in various problems of mathematical physics and mechanics.


Smirnov, V. I. Kurs vysshei matematiki, 6th ed., vol. 3, part 2. Moscow-Leningrad, 1957.
Whittaker, E. T., and G. N. Watson. Kurs sovremennogo analiza, 2nd ed., part 2. Moscow, 1963. (Translated from English.)