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Asymptotic and numeric study of eigenvalues of the double confluent Heun equation. (English) Zbl 0949.34069
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.
34L16Numerical approximation of eigenvalues and of other parts of the spectrum
65L15Eigenvalue problems for ODE (numerical methods)
34E05Asymptotic expansions (ODE)
34B05Linear boundary value problems for ODE
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
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