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ON SPECTRAL POLYNOMIALS OF THE HEUN EQUATION. I
Stockholm University, Faculty of Science, Department of Mathematics.
Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sci- ences, 250 68 ˇ Reˇz near Prague, Czech Republic .
2010 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 162, no 4, 766-781 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 162, no 4, 766-781 p.
Keyword [en]
Heun equation, Spectral polynomials, Asymptotic root distribution
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-49768ISI: 000276696200009OAI: oai:DiVA.org:su-49768DiVA: diva2:379399
Note
authorCount :2Available from: 2010-12-31 Created: 2010-12-17 Last updated: 2017-12-11Bibliographically approved

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