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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.

 

How to Cite this Article:
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.