Binomial series and complex difference equations
Binomial series and complex difference equations
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DOI：
10.1016/j.jmaa.2020.124844
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发表时间：
2019-08
影响因子：
1.3
通讯作者：
K. Ishizaki;Z. Wen
中科院分区：
文献类型：
--
作者：
K. Ishizaki;Z. Wen
本文研究了二项级数∑ n= 0∞ an z n _，其中z n _= z（z− 1）<$（z− n+ 1）的性质，以及二项级数在复域上的收敛性.讨论了一类用二项式级数表示的差分方程的整体解和亚纯解的增长级。提供了一些例子。作为应用，我们构造了一个具有1/2阶超越亚纯解的差分Riccati方程。
In this study, we consider the properties of binomial series∑ n= 0∞ a n z n _, where z n _= 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.