Some q-generating functions of the Carlitz and Srivastava-Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers-Szegö polynomials
Some q-generating functions of the Carlitz and Srivastava-Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers-Szegö polynomials
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DOI：
10.1016/j.amc.2013.01.065
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
Jianbing Cao;H. Srivastava
中科院分区：
文献类型：
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作者：
Jianbing Cao;H. Srivastava
Motivated essentially by the fact that generating functions play an important rôle in the investigation of many potentially useful properties of the sequences which they generate, various families of q-generating functions of the Carlitz and Srivastava–Agarwal types have been investigated in the literature for the continuous q-Hermite polynomials, the Hahn polynomials, the Rogers–Szegö polynomials, and indeed also for many other q-polynomial systems. The main object of this paper is to apply a certain q-exponential decomposition technique with a view to deriving several bilinear and trilinear q-generating functions associated with the generalized Hahn polynomials. As a simple consequence of one of the main results derived in this paper, we are led naturally to the corrected version of a bilinear q-generating function which appeared in one of Carlitz’s papers.
