A q-analogue of Kummer's equation
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 equa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/31/abstr.html |
| Summary: | 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 ${}_1\Phi_1$. |
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| ISSN: | 1072-6691 |