## Finite order meromorphic solutions of linear difference equations.(English)Zbl 1226.30032

Summary: We mainly investigate the growth and the value distribution of meromorphic solutions of the linear difference equation $a_{n}(z)f(z+n)+\cdots +a_{1}(z)f(z+1)+a_{0}(z)f(z)=b(z),$ where $$a_{0}(z),a_{1}(z),\dots,a_{n}(z),b(z)$$ are entire functions such that $$a_{0}(z)a_{n}(z)\not\equiv 0$$. For a finite order meromorphic solution $$f(z)$$, some interesting results on the relation between $$\rho=\rho(f)$$ and $$\lambda_{f}=\max\{\lambda(f),\lambda(1/f)\}$$, are proved. Examples are provided for our results.

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 39A13 Difference equations, scaling ($$q$$-differences) 39A22 Growth, boundedness, comparison of solutions to difference equations

### Keywords:

difference equations; value distribution; finite order
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### References:

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