Eigenvalue Problems for Lam\'e's Differential Equation
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🧮 math.CA
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eigenvaluecasesdifferentiale-wangerinequationfunctionsgeneralizedproblem
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The Floquet eigenvalue problem and a generalized form of the Wangerin eigenvalue problem for Lam\'e's differential equation are discussed. Results include comparison theorems for eigenvalues and analytic continuation, zeros and limiting cases of (generalized) Lam\'e-Wangerin eigenfunctions. Algebraic Lam\'e functions and Lam\'e polynomials appear as special cases of Lam\'e-Wangerin functions.
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