Meromorphic functions of finite $\varphi$-order and linear Askey-Wilson divided difference equations

TL;DR

This paper estimates the growth of meromorphic solutions to linear difference equations involving Askey-Wilson divided difference operators using the $\

Contribution

It introduces the use of $\\varphi$-order as a growth measure, bridging the gap between logarithmic and classical orders for meromorphic functions.

Findings

Growth estimates for solutions are provided.

The $\\varphi$-order effectively characterizes solution behavior.

The approach generalizes classical growth measures.

Abstract

The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The $\varphi$-order is used as a general growth indicator, which covers the growth spectrum between the logarithmic order $\rho_{\log}(f)$ and the classical order $\rho(f)$ of a meromorphic function $f$.