Abstract
AbstractIn this paper, by making use of the familiar q-difference operators $D_{q}$
D
q
and $D_{q^{-1}}$
D
q
−
1
, we first introduce two homogeneous q-difference operators $\mathbb{T}(\mathbf{a},\mathbf{b},cD_{q})$
T
(
a
,
b
,
c
D
q
)
and $\mathbb{E}(\mathbf{a},\mathbf{b}, cD_{q^{-1}})$
E
(
a
,
b
,
c
D
q
−
1
)
, which turn out to be suitable for dealing with the families of the generalized Al-Salam–Carlitz q-polynomials $\phi_{n}^{(\mathbf{a},\mathbf{b})}(x,y|q)$
ϕ
n
(
a
,
b
)
(
x
,
y
|
q
)
and $\psi_{n}^{(\mathbf{a},\mathbf{b})}(x,y|q)$
ψ
n
(
a
,
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference31 articles.
1. CBMS Reg. Conf. Ser. Math.;G.E. Andrews,1986
2. Gasper, G., Rahman, M.: Basic Hypergeometric Series, 2nd edn. Cambridge University Press, Cambridge (2004)
3. González, B., Matera, J., Srivastava, H.M.: Some q-generating functions and associated families of generalized hypergeometric polynomials. Math. Comput. Model. 34(1–2), 133–175 (2001)
4. Medem, J.C., Álvarez-Nodarse, R., Marcellán, F.: On the q-polynomials: a distributional study. J. Comput. Appl. Math. 135(2), 157–196 (2001)
5. Srivastava, H.M., Manocha, H.L.: A Treatise on Generating Functions. Ellis Horwood, Chichester (1984)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献