论文标题
为某些广义的al-Salam-Carlitz $ Q $ -Polynomials生成功能
Generating Functions for Some Families of the Generalized Al-Salam-Carlitz $q$-Polynomials
论文作者
论文摘要
在本文中，通过利用熟悉的$ q $ -difference运算符$ d_q $和$ d_ {q^{ - 1}} $，我们首先介绍两个同质$ q $ -Difference Operator $ \ Mathbb {t}（t}（t}） a}，{\ bf b}，cd_ {q^{ - 1}}）$，最适合与广义的al-salam-carlitz $ q $ -polyNomials $ d ϕ_n^^{ $ψ_n^{（{\ bf a}，{\ bf b}）}（x，y | q）$。然后，我们将这两个同质$ q $ - 差异运算符应用于生成功能，Rogers类型公式，扩展的Rogers类型公式和Srivastava-Agarwal型线性以及双线性生成功能，这些功能涉及这些广义的Al-Salam-Salam-Salam-Salam-carlitz $ Q $ Q-Q-Q-POLYS的这些家族。我们还展示了此处介绍的各种结果与我们在本文中研究的许多较早作品中的各种结果如何相关。
In this paper, by making use of the familiar $q$-difference operators $D_q$ and $D_{q^{-1}}$, we first introduce two homogeneous $q$-difference operators $\mathbb{T}({\bf a},{\bf b},cD_q)$ and $\mathbb{E}({\bf a},{\bf b}, cD_{q^{-1}})$, which turn out to be suitable for dealing with the families of the generalized Al-Salam-Carlitz $q$-polynomials $ϕ_n^{({\bf a},{\bf b})}(x,y|q)$ and $ψ_n^{({\bf a},{\bf b})}(x,y|q)$. We then apply each of these two homogeneous $q$-difference operators in order to derive generating functions, Rogers type formulas, the extended Rogers type formulas and the Srivastava-Agarwal type linear as well as bilinear generating functions involving each of these families of the generalized Al-Salam-Carlitz $q$-polynomials. We also show how the various results presented here are related to those in many earlier works on the topics which we study in this paper.
