Meromorphic functions of finite $\varphi$-order and linear $q$-difference equations
Complex Variables
2020-10-26 v1
Abstract
The -order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex plane are investigated in terms of the -order, which measures the growth of functions between the classical order and the logarithmic order. Several results on value distribution of meromorphic functions are discussed by using the -order and the -exponent of convergence. Instead of linear differential equations, the applications in the complex plane lie in linear -difference equations.
Cite
@article{arxiv.2010.12356,
title = {Meromorphic functions of finite $\varphi$-order and linear $q$-difference equations},
author = {Janne Heittokangas and Jun Wang and Zhi-Tao Wen and Hui Yu},
journal= {arXiv preprint arXiv:2010.12356},
year = {2020}
}
Comments
28 pages