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arxiv: math/0311307 · v5 · submitted 2003-11-18 · 🧮 math.CA · math-ph· math.MP· nlin.SI

Analytic continuation of eigenvalues of the Lam\'e operator

classification 🧮 math.CA math-phmath.MPnlin.SI
keywords eigenvaluesbranchingoperatoranalyticclarifycomplex-analyticcontinuationconvergent
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Eigenvalues of the Lam\'e operator are studied as complex-analytic functions in period $\tau$ of an elliptic function. We investigate the branching of eigenvalues numerically and clarify the relationship between the branching of eigenvalues and the convergent radius of a perturbation series.

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