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Zbl 1076.33014
Volkmer, Hans
Four remarks on eigenvalues of Lamé's equation. (English)
[J] Anal. Appl., Singap. 2, No. 2, 161-175 (2004). ISSN 0219-5305

The paper under review focuses on four aspects of the eigenvalues $h$ of Lamé's equation $$\frac{d^2w}{dx^2}+(h-\nu(\nu+1)k^2\text{sn}^2(x,k))w=0,$$ where $0<k<1$, $\nu\ge-\frac{1}{2}$, and $\text{sn}(x,k)$ is the Jacobi elliptic function with modulus $k$. The four aspects are: interlacing properties, behavior as $k\to 1$, width of stability bands as $\nu\to\infty$, and expansion in powers of $k^2$.
[Daniel Beltiţă (Bucureşti)]

MSC 2000:: *33E10 Spheroidal wave functions, etc.
34B30 Special ODE

Keywords: Lamé's equation; stability bands

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