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Matem. Mod., 2015, Volume 27, Number 7, Pages 111–116 (Mi mm3630)  

Evaluation of eigenvalues and eigenfunctions of Coulomb spheroidal wave equation

S. L. Skorokhodov

Dorodnicyn Computing Centre of RAS, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00923
Russian Academy of Sciences - Federal Agency for Scientific Organizations


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Received: 30.03.2015

Citation: S. L. Skorokhodov, “Evaluation of eigenvalues and eigenfunctions of Coulomb spheroidal wave equation”, Matem. Mod., 27:7 (2015), 111–116

Citation in format AMSBIB
\Bibitem{Sko15}
\by S.~L.~Skorokhodov
\paper Evaluation of eigenvalues and eigenfunctions of Coulomb spheroidal wave equation
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 7
\pages 111--116
\mathnet{http://mi.mathnet.ru/mm3630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3545734}
\elib{https://elibrary.ru/item.asp?id=24850065}


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