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On difference Riccati equations and second order linear difference equations. (English) Zbl 1215.39021

The author considers second order linear difference equations and the associated difference Riccati equation in the complex domain, namely

${{\Delta }}^{2}y\left(z\right)+A\left(z\right)y\left(z\right)=0$

and

${\Delta }f\left(z\right)=\frac{f{\left(z\right)}^{2}+A\left(z\right)}{f\left(z\right)-1}$

where he defines

${\Delta }\varphi \left(z\right)=\varphi \left(z+1\right)-\varphi \left(z\right)$

with the standard iteration of the difference operator; $A\left(z\right)$ is a meromorphic function. He considers: meromorphic solutions of the difference Riccati equation and the discrete analogue of the cross ratio; linear second order difference equations in the complex domain and growth problems for the solutions.

##### MSC:
 39A45 Difference equations in the complex domain 39A13 Difference equations, scaling ($q$-differences) 39A06 Linear equations (difference equations) 30D15 Special classes of entire functions; growth estimates
##### References:
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