29 Lamé Functions Lamé Functions 29.10 Lamé Functions with Imaginary Periods 29.12 Definitions

§29.11 Lamé Wave Equation

Keywords:: Lamé wave equation, ellipsoidal wave equation
Permalink:: http://dlmf.nist.gov/29.11

The Lamé (or ellipsoidal) wave equation is given by

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

Symbols:: $\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)$ : Jacobian elliptic function, $\frac{df}{dx}$ : derivative of with respect to , : complex variable, : real parameter, : real parameter, $\nu$ : real parameter, $\omega$ : parameter and : solution
Referenced by:: §29.11, §29.11, §29.18(ii), §29.7(ii)
Permalink:: http://dlmf.nist.gov/29.11.E1
Encodings:: TeX, pMML, png

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).

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 29.10 Lamé Functions with Imaginary Periods 29.12 Definitions