Geodesic
Evaluation of eigenvalues and eigenfunctions of Coulomb spheroidal wave equation
Matematičeskoe modelirovanie, Tome 27 (2015) no. 7, pp. 111-116

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A method for evaluation the eigenvalues $\lambda_{m,q}(b,c)$ and the eigenfunctions of Coulomb spheroidal wave equation in a case of complex parameters $b$ and $c$ is proposed. The method is based on construction of two expansions of solution at the singular points $\eta=\pm1$ and on matching of the expansions at the point $\eta=0$. Numerical experiments show that there exist branching points of the eigenvalues $\lambda_{m,q}(b,c)$ for some complex values $b$ or $c$, the order of the branching points is equal $2$.
Keywords: Coulomb spheroidal wave functions, complex parameters, evaluation of eigenvalues, branching points. 
@article{MM_2015_27_7_a16,
     author = {S. L. Skorokhodov},
     title = {Evaluation of eigenvalues and eigenfunctions of {Coulomb} spheroidal wave equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {111--116},
     publisher = {mathdoc},
     volume = {27},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_7_a16/}
}
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S. L. Skorokhodov. Evaluation of eigenvalues and eigenfunctions of Coulomb spheroidal wave equation. Matematičeskoe modelirovanie, Tome 27 (2015) no. 7, pp. 111-116. http://geodesic.mathdoc.fr/item/MM_2015_27_7_a16/