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Four remarks on eigenvalues of Lamé’s equation. (English) Zbl 1076.33014
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 $k^2$.

33E10Lamé, Mathieu, and spheroidal wave functions
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
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