Abstract
In this paper, we establish one general q-exponential operator identity by solving one simple q-difference equation. Using this q-difference equation, we get some generalizations of Andrews-Askey and Askey-Wilson integral. In addition, we also discuss some properties of q-polynomials H n .MSC:33D05, 33D45, 11B65, 33D60.
Highlights
1 Introduction and notations For decades, various families of q-polynomials and q-integral have been investigated rather widely and extensively due mainly to their having been found to be potentially useful in such wide variety of fields as theory of partitions, number theory, combinatorial analysis, finite vector spaces, Lie theory, etc
We adopt the notations used by Gasper and Rahman [ ]
Replacing n – by n, applying ( ), we find that the above equation is equal to c(bw; q)∞∞
Summary
Introduction and notationsFor decades, various families of q-polynomials and q-integral have been investigated rather widely and extensively due mainly to their having been found to be potentially useful in such wide variety of fields as theory of partitions, number theory, combinatorial analysis, finite vector spaces, Lie theory, etc. (cf. [ – ]). Bs, b, c ∈ C, we define the following generalized q-operator: F(a , . We present the following more generalized q-difference equation for the above q-operator.
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