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Zbl 0949.34069
Lay, W.; Bay, K.; Slavyanov, S.Yu.
Asymptotic and numeric study of eigenvalues of the double confluent Heun equation. (English)
[J] J. Phys. A, Math. Gen. 31, No.42, 8521-8531 (1998). ISSN 0305-4470

The authors give an asymptotic study resulting in the eigenfunctions and eigenvalues, which arise in the central two-point connection problem of the two singularities along the real axis. Thereafter a numeric procedure for computing the eigenvalues is proposed. It is based on an extension of Jaffacutee expansions introduced by Lay and on an algorithm and programming code developed by {\it K. Bay} and {\it W. Lay} [J. Math. Phys. 38, No. 5, 2127-2131 (1997; Zbl 0876.34080)]. Also they discover a finite set of generalized polynomial solutions for certain combinations of the parameters.
[N.V.Grigorenko (Ky{\" i}v)]

MSC 2000:: *34L16 Numerical approximation of eigenvalues, etc.
65L15 Eigenvalue problems for ODE (numerical methods)
34E05 Asymptotic expansions (ODE)
34B05 Linear boundary value problems of ODE
34L15 Estimation of eigenvalues for OD operators

Keywords: Jaffacutee expansions

Citations: Zbl 0876.34080

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