Abstract
In this study, we consider the properties of binomial series ∑n=0∞anzn_, where zn_=z(z−1)⋯(z−n+1), and the convergence of binomial series in the complex domain. We discuss the order of growth for the entire and meromorphic solutions of some difference equations represented by binomial series. Some examples are provided. As an application, we construct a difference Riccati equation that possesses a transcendental meromorphic solution of order 1/2.
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