## Hari M. Srivastava, Sama Arjika, Abey Sherif Kelil, Some homogeneous q-difference operators and the associated generalized Hahn polynomials

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DOI: 10.23952/asvao.1.2019.2.07
Volume 1, Issue 2, 31 August 2019, Pages 187-201

Abstract. In this paper, we first construct the homogeneous $q$-shift operator $\widetilde{E}(a,b;D_{q})$ and the homogeneous $q$-difference operator $\widetilde{L}(a,b;\Theta_{x,y})$. We then apply these operators in order to represent and investigate a family of generalized Cauchy polynomials and a general form of the $q$-Hahn polynomials. We derive some $q$-identities such as generating functions, extended generating functions, Mehler’s formula and Rogers’ formula for these $q$-polynomials. Relevant connections of the $q$-identities presented here with a number of known or new results associated with various specialized families of $q$-polynomials are also considered.

Hari M. Srivastava, Sama Arjika, Abey Sherif Kelil, Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials, Appl. Set-Valued Anal. Optim. 1 (2019), 187-201.