On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations

We consider q-difference Riccati equations and second-order linear q-difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q-difference Riccati e...

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Bibliographic Details
Published in:Journal of Complex Analysis 2013-01, Vol.2013 (2013), p.1-10
Main Author: Huang, Zhi-Bo
Format: Article
Language:English
Subjects:
Difference equations
Gamma function
Mathematical analysis
Riccati equation
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Summary:We consider q-difference Riccati equations and second-order linear q-difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q-difference Riccati equations, and the q-Casorati determinant of meromorphic solutions of second-order linear q-difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the q-Gamma function when q∈ℂ such that 0
ISSN:2314-4963
2314-4971
DOI:10.1155/2013/938579