Eigenvalue Problems for Lamé's Differential Equation

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.