Carlitz's q-Operators for the Generalized Homogeneous Hahn Polynomials
Corresponding Author
Jian Cao
School of Mathematics, Hangzhou Normal University, Hangzhou, China
Correspondence:
Jian Cao ([email protected])
Contribution: Conceptualization, Methodology, Writing - original draft, Supervision
Search for more papers by this authorH. M. Srivastava
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, China
Center for Converging Humanities, Kyung Hee University, Seoul, Republic of Korea
Department of Applied Mathematics, Chung Yuan Christian University, Taoyuan City, Taiwan
Department of Mathematics and Informatics, Azerbaijan University, Baku, Azerbaijan
Section of Mathematics, International Telematic University Uninettuno, Rome, Italy
Search for more papers by this authorYue Zhang
School of Mathematics, Hangzhou Normal University, Hangzhou, China
Contribution: Writing - original draft, Formal analysis
Search for more papers by this authorCorresponding Author
Jian Cao
School of Mathematics, Hangzhou Normal University, Hangzhou, China
Correspondence:
Jian Cao ([email protected])
Contribution: Conceptualization, Methodology, Writing - original draft, Supervision
Search for more papers by this authorH. M. Srivastava
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, China
Center for Converging Humanities, Kyung Hee University, Seoul, Republic of Korea
Department of Applied Mathematics, Chung Yuan Christian University, Taoyuan City, Taiwan
Department of Mathematics and Informatics, Azerbaijan University, Baku, Azerbaijan
Section of Mathematics, International Telematic University Uninettuno, Rome, Italy
Search for more papers by this authorYue Zhang
School of Mathematics, Hangzhou Normal University, Hangzhou, China
Contribution: Writing - original draft, Formal analysis
Search for more papers by this authorABSTRACT
In this paper, motivated by Carlitz's -operators and Liu's generalized homogeneous Hahn polynomials, we show how to construct Carlitz's -operators of the generalized homogeneous Hahn polynomials. We derive several generating functions for the generalized homogeneous Hahn polynomials by applying the method of exponential operator decomposition. In addition, we deduce Rogers type bilinear, trilinear, and mixed-type generating functions as well as the Srivastava–Agarwal-type generating functions for the generalized homogeneous Hahn polynomials, which provide extensions of the results of Carlitz, Abdlhusein, and Saad and Abdlhusein.
Conflicts of Interest
The authors declare no conflicts of interest.
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