A q-analogue of Kummer's equation
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Date
2017-01-29
Authors
Jia, Lukun
Feng, Zhaosheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
q-Analogue, Kummer's equation, Frobenius method, Contiguous relations
Citation
Jia, L., Cheng, J., & Feng, Z. (2017). A q-analogue of Kummer's equation. Electronic Journal of Differential Equations, 2017(31), pp. 1-20.
Rights
Attribution 4.0 International