Growth and value distribution of linear difference polynomials generated by meromorphic solutions of higher-order linear difference equations
DOI:
https://doi.org/10.58997/ejde.2023.84Keywords:
Linear difference equation; linear difference polynomial; meromorphic solution; growth; value distributionAbstract
In this article, we investigate the relationship between growth and value distribution of meromorphic solutions for the higher-order complex linear difference equations $$ A_n(z)f(z+n)+\dots+A_1(z)f(z+1)+A_0(z)f(z)=0 \quad \text{and } =F(z), $$ and for the linear difference polynomial $$ g(z)=\alpha_n(z)f(z+n)+\dots+\alpha_1(z)f(z+1)+\alpha_0(z)f(z) $$ generated by \(f(z)\) where \(A_j(z)\), \(\alpha_j(z)\) (\(j=0,1,\ldots,n\)), \(F(z)\) \((\not\equiv0)\) are meromorphic functions. We improve some previous results due to Belaidi, Chen and Zheng and others.
For more information see https://ejde.math.txstate.edu/Volumes/2023/84/abstr.html
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Copyright (c) 2023 Yi Xin Luo, Xiu Min Zheng
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