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- Title
A Q-ANALOGUE OF KUMMER'S EQUATION.
- Authors
LUKUN JIA; JINFA CHENG; ZHAOSHENG FENG
- 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.
- Subjects
KUMMER surfaces; FROBENIUS algebras; INTEGRALS; CHARACTERISTIC functions; HYPERGEOMETRIC series
- Publication
Electronic Journal of Differential Equations, 2017, Vol 2017, Issue 1-54, p1
- ISSN
1550-6150
- Publication type
Article