# §29.11 Lamé Wave Equation

The Lamé (or ellipsoidal) wave equation is given by

 29.11.1 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(h-\nu(\nu+1)k^{2}{\operatorname{% sn}^{2}}\left(z,k\right)+k^{2}\omega^{2}{\operatorname{sn}^{4}}\left(z,k\right% ))w=0,$

in which $\omega$ is another parameter. In the case $\omega=0$, (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).