A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials
This article presents the theory of trivariate <i>q</i>-truncated Gould–Hopper polynomials through a generating function approach utilizing <i>q</i>-calculus functions. These polynomials are subsequently examined within the framework of quasi-monomiality, leading to the estab...
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2025-06-01
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| author | Waseem Ahmad Khan Khidir Shaib Mohamed Francesco Aldo Costabile Can Kızılateş Cheon Seoung Ryoo |
| author_facet | Waseem Ahmad Khan Khidir Shaib Mohamed Francesco Aldo Costabile Can Kızılateş Cheon Seoung Ryoo |
| author_sort | Waseem Ahmad Khan |
| collection | DOAJ |
| description | This article presents the theory of trivariate <i>q</i>-truncated Gould–Hopper polynomials through a generating function approach utilizing <i>q</i>-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 <i>q</i>-differential and partial differential equations are formulated for the trivariate <i>q</i>-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 <i>q</i>-truncated Gould–Hopper polynomials and their potential applications. |
| format | Article |
| id | doaj-art-54b79fab804b4b198021b1dcb418dc6c |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-54b79fab804b4b198021b1dcb418dc6c2025-08-20T03:16:22ZengMDPI AGMathematics2227-73902025-06-011312196410.3390/math13121964A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General PolynomialsWaseem Ahmad Khan0Khidir Shaib Mohamed1Francesco Aldo Costabile2Can Kızılateş3Cheon Seoung Ryoo4Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, ItalyDepartment of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100 Zonguldak, TurkeyDepartment of Mathematics, Hannam University, Daejeon 34430, Republic of KoreaThis article presents the theory of trivariate <i>q</i>-truncated Gould–Hopper polynomials through a generating function approach utilizing <i>q</i>-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 <i>q</i>-differential and partial differential equations are formulated for the trivariate <i>q</i>-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 <i>q</i>-truncated Gould–Hopper polynomials and their potential applications.https://www.mdpi.com/2227-7390/13/12/1964quantum calculus<i>q</i>-truncated polynomials<i>q</i>-truncated-Gould-Hopper polynomials<i>q</i>-quasi monomialityfractional derivativesdifferential equations |
| spellingShingle | Waseem Ahmad Khan Khidir Shaib Mohamed Francesco Aldo Costabile Can Kızılateş Cheon Seoung Ryoo A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials Mathematics quantum calculus <i>q</i>-truncated polynomials <i>q</i>-truncated-Gould-Hopper polynomials <i>q</i>-quasi monomiality fractional derivatives differential equations |
| title | A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials |
| title_full | A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials |
| title_fullStr | A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials |
| title_full_unstemmed | A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials |
| title_short | A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials |
| title_sort | new generalization of i q i truncated polynomials associated with i q i general polynomials |
| topic | quantum calculus <i>q</i>-truncated polynomials <i>q</i>-truncated-Gould-Hopper polynomials <i>q</i>-quasi monomiality fractional derivatives differential equations |
| url | https://www.mdpi.com/2227-7390/13/12/1964 |
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