q-Difference equations for generalized homogeneous q-operators and certain generating functions
q-Difference equations for generalized homogeneous q-operators and certain generating functions
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DOI：
10.1080/10236198.2013.823955
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发表时间：
2014-05
影响因子：
1.1
通讯作者：
Jianbing Cao
中科院分区：
文献类型：
--
作者：
Jianbing Cao
本文给出了两个由q-差分方程得到的广义齐次q-算子恒等式。此外，我们推广了Chen等人[W.Y.C. Chen，中国山核桃A. M. Fu和B。Zhang，齐次q-差分算子，Adv. Appl. Math. 31（2003），pp. 659-668]和萨阿德和苏克希[H. L. Saad和A.A. Sukhi，另一种齐次q-差分算子，应用数学计算。215（2010），pp. 4332-4339]通过q-差分方程的方法。利用q-差分方程得到了Verma-Jain多项式生成函数的U（n+1）推广.最后，我们利用q-差分方程得到了两个变换恒等式。
In this paper, we give two generalized homogeneous q-operator identities, which are obtained by q-difference equations. In addition, we generalize certain generating functions from Chen et al. [W.Y.C. Chen, A. M. Fu, and B. Zhang, The homogeneous q-difference operator, Adv. Appl. Math. 31 (2003), pp. 659–668] and Saad and Sukhi [H. L. Saad and A.A. Sukhi, Another homogeneous q-difference operator, Appl. Math. Comput. 215 (2010), pp. 4332–4339] by the method of q-difference equations. Moreover, we gain U(n+1) generalizations of generating functions for Verma–Jain polynomials by q-difference equations. Finally, we obtain two transformational identities by q-difference equations.