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On spectral polynomials of the Heun equation. I

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    0343020 - ÚJF 2011 RIV US eng J - Journal Article
    Shapiro, B. - Tater, Miloš
    On spectral polynomials of the Heun equation. I.
    Journal of Approximation Theory. Roč. 162, č. 4 (2010), s. 766-781. ISSN 0021-9045. E-ISSN 1096-0430
    R&D Projects: GA MŠk LC06002
    Institutional research plan: CEZ:AV0Z10480505
    Keywords : Heun equation * Spectral polynomials * Asymptotic root distribution
    Subject RIV: BE - Theoretical Physics
    Impact factor: 0.710, year: 2010

    The classical Heun equation has the form {Q(z)d(2)/dz(2) + P(z)d/dz + V(z)} S(z) = 0. where Q(z) is a cubic complex polynomial, P(z) is a polynomial of degree at most 2 and V(z) is at most linear. In the second half of the nineteenth century E. Heine and T. Stieltjes initiated the study of the set of all V(z) for which the above equation has a polynomial solution S(z) of a given degree n. The main goal of the present paper is to study the union of the roots of the latter set of V(z)'s when n -> infinity. We provide an explicit description of this limiting set and give a substantial amount of preliminary and additional information about it obtained using a certain technique developed by A.B.J. Kuijlaars and W. Van Assche.
    Permanent Link: http://hdl.handle.net/11104/0185599

     
     
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