Lacunary Generating Functions of Hybrid Type Polynomials in Viewpoint of Symbolic Approach
  • Nusrat Raza1, Umme Zainab2 and Serkan Araci3,*
1Mathematics Section, Women’ s College, Aligarh Muslim University, Aligarh, 202002, India
2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
3Department of Economics, Faculty of Economics, Administrative of Social Sciences, Hasan Kalyoncu University, Gaziantep, TR-27410, Turkey
*Corresponding Author: Serkan Araci. Email: serkan.araci@hku.edu.tr
(This article belongs to this Special Issue:Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)
Received 29 May 2021; Accepted 19 August 2021 ; Published online 30 September 2021
Abstract
In this paper, we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials. We obtain the series definitions of these hybrid special polynomials. Also, we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials. Further, we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials. Some concluding remarks are also given.
Keywords
Hermite-laguerre polynomials; laguerre-wright polynomials; hermite-laguerre-wright polynomials hermite-mittag-leffler functions