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

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  • Zhi-Bo Huang

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.

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  • Zhi-Bo Huang, 2013. "On -Difference Riccati Equations and Second-Order Linear -Difference Equations," Journal of Complex Analysis, Hindawi, vol. 2013, pages 1-10, January.
    • Handle: RePEc:hin:jnljca:938579
    DOI: 10.1155/2013/938579
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