On generalized Heun equation with some mathematical properties
dc.contributor.author | Saad, Nasser | |
dc.date.accessioned | 2022-05-04T12:02:27Z | |
dc.date.available | 2022-05-04T12:02:27Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Acta Polytechnica. 2022, vol. 62, no. 1, p. 165-189. | |
dc.identifier.issn | 1210-2709 (print) | |
dc.identifier.issn | 1805-2363 (online) | |
dc.identifier.uri | http://hdl.handle.net/10467/100617 | |
dc.description.abstract | We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters. The existence conditions for the polynomial solutions are given. A simple procedure based on a recurrence relation is introduced to evaluate these polynomial solutions explicitly. For α0 = 0, α1≠ 0, we prove that the polynomial solutions of the corresponding differential equation are sources of finite sequences of orthogonal polynomials. Several mathematical properties, such as the recurrence relation, Christoffel-Darboux formulas and the norms of these polynomials, are discussed. We shall also show that they exhibit a factorization property that permits the construction of other infinite sequences of orthogonal polynomials. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | České vysoké učení technické v Praze | cs |
dc.publisher | Czech Technical University in Prague | en |
dc.relation.ispartofseries | Acta Polytechnica | |
dc.relation.uri | https://ojs.cvut.cz/ojs/index.php/ap/article/view/7583 | |
dc.rights | Creative Commons Attribution 4.0 International License | en |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.title | On generalized Heun equation with some mathematical properties | |
dc.type | article | en |
dc.date.updated | 2022-05-04T12:02:27Z | |
dc.identifier.doi | 10.14311/AP.2022.62.0165 | |
dc.rights.access | openAccess | |
dc.type.status | Peer-reviewed | |
dc.type.version | publishedVersion |
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