On spectral polynomials of the Heun equation
| dc.creator | Shapiro, B. | |
| dc.creator | Tater, M. | |
| dc.date | 2008-12-12 | |
| dc.date.accessioned | 2026-07-07T12:12:24Z | |
| dc.date.available | 2026-07-07T12:12:24Z | |
| dc.description | 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, P(z) at most quadratic and V(z) linear polynomials resp. In the second half of the 19-th century E.Heine and T.STieltjes initiated the study of the set of all V(z) such that 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->oo. We formulate an intriguing conjecture of K.Takemura describing the limiting set and give a substantial amount of additional information. | |
| dc.description | 14 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0812.2321 | |
| dc.identifier | http://arxiv.org/abs/0812.2321 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210531 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34L20 (Primary), 30C15, 33E05 (Secondary) | |
| dc.title | On spectral polynomials of the Heun equation | |
| dc.type | text |