A q-analogue of Kummer's equation
| dc.contributor.author | Jia, Lukun | |
| dc.contributor.author | Feng, Zhaosheng | |
| dc.date.accessioned | 2022-03-22T16:37:31Z | |
| dc.date.available | 2022-03-22T16:37:31Z | |
| dc.date.issued | 2017-01-29 | |
| dc.description.abstract | In this article we define a q-analogue of Kummer's equation. It has two singular points. Near the singular point at zero, using the Frobenius method, we obtain two linearly independent series solutions in any one of three cases according to the difference of roots of the characteristic equation. Near the singular point at infinity, given that the only formal series solution is divergent, we find two integral solutions which are convergent under some condition. Finally, using the q-analogue of Kummer's equation, we deduce six contiguous relations about the q-hypergeometric series 1Φ1. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Jia, L., Cheng, J., & Feng, Z. (2017). A q-analogue of Kummer's equation. <i>Electronic Journal of Differential Equations, 2017</i>(31), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15536 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | q-Analogue | |
| dc.subject | Kummer's equation | |
| dc.subject | Frobenius method | |
| dc.subject | Contiguous relations | |
| dc.title | A q-analogue of Kummer's equation | |
| dc.type | Article |