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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Original Russian Text © S.L. Skorokhodov, D.V. Khristoforov, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 11, pp. 1880–1897.
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Skorokhodov, S.L., Khristoforov, D.V. Calculating the branch points of the eigenvalues of the Coulomb spheroidal wave equation. Comput. Math. and Math. Phys. 47, 1802–1818 (2007). https://doi.org/10.1134/S0965542507110073
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DOI: https://doi.org/10.1134/S0965542507110073