On factorization of $q$-difference equation for continuous $q$-ultraspherical polynomials
| dc.creator | Area, I. | |
| dc.creator | Atakishiyeva, M. K. | |
| dc.creator | Rodal, J. | |
| dc.date | 2007-04-24 | |
| dc.date.accessioned | 2026-07-07T07:57:56Z | |
| dc.date.available | 2026-07-07T07:57:56Z | |
| dc.description | We prove that a customary Sturm-Liouville form of second-order $q$-difference equation for the continuous $q$-ultraspherical polynomials $C_n(x;β| q)$ of Rogers can be written in a factorized form in terms of some explicitly defined $q$-difference operator ${\mathcal D}_x^{β, q}$. This reveals the fact that the continuous $q$-ultraspherical polynomials $C_n(x;β| q)$ are actually governed by the $q$-difference equation ${\mathcal D}_x^{β, q} C_n(x;β| q)= (q^{-n/2}+βq^{n/2}) C_n(x;β| q)$, which can be regarded as a square root of the equation, obtained from its original form. | |
| dc.identifier | https://arxiv.org/abs/0704.3123 | |
| dc.identifier | http://arxiv.org/abs/0704.3123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127831 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 33D45, 39A13 | |
| dc.title | On factorization of $q$-difference equation for continuous $q$-ultraspherical polynomials | |
| dc.type | text |