Eigenvalue Problems for Lamé's Differential Equation

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.