On solutions of the q-hypergeometric equation with q^{N}=1
| dc.creator | Takeyama, Yoshihiro | |
| dc.date | 2001-06-07 | |
| dc.date.accessioned | 2026-07-07T04:42:01Z | |
| dc.date.available | 2026-07-07T04:42:01Z | |
| dc.description | We consider the q-hypergeometric equation with q^{N}=1 and $α, β, γ\in {\Bbb Z}$. We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is two-dimensional over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function of the Barnes type constructed by Nishizawa and Ueno. Then we see that this function has logarithmic singularity at the origin. This is a difference between the q-hypergeometric functions with 0<|q|<1 and at |q|=1. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0106041 | |
| dc.identifier | http://arxiv.org/abs/math/0106041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61599 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | On solutions of the q-hypergeometric equation with q^{N}=1 | |
| dc.type | text |