Calculating the branch points of the eigenvalues of the Coulomb spheroidal wave equation |
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Authors: | S L Skorokhodov D V Khristoforov |
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Institution: | (1) Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia;(2) Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | A method for computing the eigenvalues λ mn (b, c) and the eigenfunctions of the Coulomb spheroidal wave equation is proposed in the case of complex parameters b and c. The solution is represented as a combination of power series expansions that are then matched at a single point. An extensive numerical analysis shows that certain b s and c s are second-order branch points for λ mn (b, c) with different indices n 1 and n 2, so that the eigenvalues at these points are double. Padé approximants, quadratic Hermite-Padé approximants, the finite element method, and the generalized Newton method are used to compute the branch points b s and c s and the double eigenvalues to high accuracy. A large number of these singular points are calculated. |
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Keywords: | Coulomb spheroidal wave functions computation of eigenvalues branch point of eigenvalues Padé approximants quadratic approximations generalized Newton method |
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