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29 Lamé FunctionsLamé Functions

§29.11 Lamé Wave Equation

The Lamé (or ellipsoidal) wave equation is given by

29.11.1 d2wdz2+(h-ν(ν+1)k2sn2(z,k)+k2ω2sn4(z,k))w=0,

in which ω is another parameter. In the case ω=0, (29.11.1) reduces to Lamé’s equation (29.2.1).

For properties of the solutions of (29.11.1) see Arscott (1956, 1959), Arscott (1964b, Chapter X), Erdélyi et al. (1955, §16.14), Fedoryuk (1989), and Müller (1966a, b, c).