A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials

Khan, Waseem Ahmad; Mohamed, Khidir Shaib; Costabile, Francesco Aldo; Kızılateş, Can; Ryoo, Cheon Seoung

doi:10.3390/math13121964

This is an early access version, the complete PDF, HTML, and XML versions will be available soon.

Open AccessArticle

A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials

by

Waseem Ahmad Khan

^1,*

,

Khidir Shaib Mohamed

^2,*

,

Francesco Aldo Costabile

^3,*,

Can Kızılateş

⁴

and

Cheon Seoung Ryoo

⁵

¹

Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia

²

Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

³

Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy

⁴

Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100 Zonguldak, Turkey

⁵

Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea

^*

Authors to whom correspondence should be addressed.

Mathematics 2025, 13(12), 1964; https://doi.org/10.3390/math13121964

Submission received: 8 May 2025 / Revised: 11 June 2025 / Accepted: 12 June 2025 / Published: 14 June 2025

(This article belongs to the Section E: Applied Mathematics)

Download Versions Notes

Abstract

This article presents the theory of trivariate q-truncated Gould–Hopper polynomials through a generating function approach utilizing q-calculus functions. These polynomials are subsequently examined within the framework of quasi-monomiality, leading to the establishment of fundamental operational identities. Operational representations are then derived, and q-differential and partial differential equations are formulated for the trivariate q-truncated Gould–Hopper polynomials. Summation formulae are presented to elucidate the analytical properties of these polynomials. Finally, graphical representations are provided to illustrate the behavior of trivariate q-truncated Gould–Hopper polynomials and their potential applications.

Keywords: quantum calculus; q-truncated polynomials; q-truncated-Gould-Hopper polynomials; q-quasi monomiality; fractional derivatives; differential equations; partial differential equations

Share and Cite

MDPI and ACS Style

Khan, W.A.; Mohamed, K.S.; Costabile, F.A.; Kızılateş, C.; Ryoo, C.S. A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials. Mathematics 2025, 13, 1964. https://doi.org/10.3390/math13121964

AMA Style

Khan WA, Mohamed KS, Costabile FA, Kızılateş C, Ryoo CS. A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials. Mathematics. 2025; 13(12):1964. https://doi.org/10.3390/math13121964

Chicago/Turabian Style

Khan, Waseem Ahmad, Khidir Shaib Mohamed, Francesco Aldo Costabile, Can Kızılateş, and Cheon Seoung Ryoo. 2025. "A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials" Mathematics 13, no. 12: 1964. https://doi.org/10.3390/math13121964

APA Style

Khan, W. A., Mohamed, K. S., Costabile, F. A., Kızılateş, C., & Ryoo, C. S. (2025). A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials. Mathematics, 13(12), 1964. https://doi.org/10.3390/math13121964

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI