Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 131, 21 pages      arXiv:1808.04877      https://doi.org/10.3842/SIGMA.2018.131

Eigenvalue Problems for Lamé's Differential Equation

Hans Volkmer
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI, 53201, USA

Received August 14, 2018, in final form December 06, 2018; Published online December 12, 2018

Abstract
The Floquet eigenvalue problem and a generalized form of the Wangerin eigenvalue problem for Lamé's differential equation are discussed. Results include comparison theorems for eigenvalues and analytic continuation, zeros and limiting cases of (generalized) Lamé-Wangerin eigenfunctions. Algebraic Lamé functions and Lamé polynomials appear as special cases of Lamé-Wangerin functions.

Key words: Lamé functions; singular Sturm-Liouville problems; tridiagonal matrices.

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