Lamé Functions

Lamé functions

[lä′mā ‚fəŋk·shənz]
(mathematics)
Functions that arise when Laplace's equation is separated in ellipsoidal coordinates.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

REFERENCES

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.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.