@article{Kang2024, 
author = {Jung Yoog Kang and Cheon Seoung Ryoo},
title = {Exploring variable-sensitive    q-difference equations for    q-SINE Euler polynomials and    q-COSINE-Euler polynomials},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {16753-16772},
keywords = {q-derivative, q-SINE Euler (QSE) polynomials, q-COSINE Euler (QCE) polynomials, q-difference equation, approximate root},
url = {https://www.sciopen.com/article/10.3934/math.2024812},
doi = {10.3934/math.2024812},
abstract = {In this study, we introduced several types of higher-order difference equations involving    q-SINE Euler (QSE) and    q-COSINE Euler (QCE) polynomials. Depending on the parameters selected, these higher-order difference equations exhibited properties of trigonometric functions or related Euler numbers. Approximate root construction focused on the QSE polynomial, which was the solution of the    q-difference equations obtained earlier. We also showed the structure of the approximate roots of higher-order polynomials among the QSE polynomials, understood them, and considered the associated conjectures.}
}