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Volume 1, Issue 2, 31 August 2019, Pages 187-201
Abstract. In this paper, we first construct the homogeneous -shift operator and the homogeneous -difference operator . We then apply these operators in order to represent and investigate a family of generalized Cauchy polynomials and a general form of the -Hahn polynomials. We derive some -identities such as generating functions, extended generating functions, Mehler’s formula and Rogers’ formula for these -polynomials. Relevant connections of the -identities presented here with a number of known or new results associated with various specialized families of -polynomials are also considered.
How to Cite this Article:
Hari M. Srivastava, Sama Arjika, Abey Sherif Kelil, Some homogeneous -difference operators and the associated generalized Hahn polynomials, Appl. Set-Valued Anal. Optim. 1 (2019), 187-201.