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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

Δ 2 y(z)+A(z)y(z)=0

and

Δf(z)=f(z) 2 +A(z) f(z)-1

where he defines

Δϕ(z)=ϕ(z+1)-ϕ(z)

with the standard iteration of the difference operator; A(z) 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:
39A45Difference equations in the complex domain
39A13Difference equations, scaling (q-differences)
39A06Linear equations (difference equations)
30D15Special classes of entire functions; growth estimates
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