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Journal of Complex Analysis
Volume 2013 (2013), Article ID 938579, 10 pages
http://dx.doi.org/10.1155/2013/938579
Research Article

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

1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland

Received 29 August 2012; Accepted 17 October 2012

Academic Editor: Yan Xu

Copyright © 2013 Zhi-Bo Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider -difference Riccati equations and second-order linear -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 -difference Riccati equations, and the -Casorati determinant of meromorphic solutions of second-order linear -difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the -Gamma function when such that . Some examples are also listed to illustrate our results.