Exploring variable-sensitive q-difference equations for q-SINE Euler polynomials and q-COSINE-Euler polynomials

Autor: Jung Yoog Kang, Cheon Seoung Ryoo
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: AIMS Mathematics, Vol 9, Iss 6, Pp 16753-16772 (2024)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.2024812?viewType=HTML
Popis: 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.
Databáze: Directory of Open Access Journals