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On spectral polynomials of the Heun equation. I
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SYSNO ASEP 0343020 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On spectral polynomials of the Heun equation. I Author(s) Shapiro, B. (SE)
Tater, Miloš (UJF-V) RID, ORCID, SAISource Title Journal of Approximation Theory. - : Elsevier - ISSN 0021-9045
Roč. 162, č. 4 (2010), s. 766-781Number of pages 16 s. Language eng - English Country US - United States Keywords Heun equation ; Spectral polynomials ; Asymptotic root distribution Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000276696200009 DOI 10.1016/j.jat.2009.09.005 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2011
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