«q-binomial theorem»

The q-Binomial Theorem and two Symmetric q-Identities

We notice two symmetric q-identities, which are special cases of the transformations of 2φ1 series in Gasper and Rahman’s book (Basic Hypergeometric Series, Cambridge University Press, 1990, p. 241). In this paper, we give combinatorial proofs of these two identities and the q-bi

Hybrid Proofs of the q-Binomial Theorem and Other Identities

We give “hybrid” proofs of the q-binomial theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as -------------------------------------------- where is a weight function, are interpolation nodes, are the corresponding weight coefficients and denotes the error term. The general form of interpolation nod

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

The $q$-Binomial Theorem and two Symmetric $q$-Identities

The q-binomial theorem and spectral symmetry

An integral generalization of the $q$-binomial theorem and an application

Applications of Some Subclasses of Meromorphic Functions Associated with the q-Derivatives of the q-Binomials

In this article, we make use of the q-binomial theorem to introduce and study two new subclasses ℵ(αq,q) ℵ(α,q) meromorphic functions in open unit disk U, that is, analytic punctured U∗=U\{0}={z:z∈Cand0<z<1}. We derive inclusion relations investigate an integral operator pr

A Noncommutative Weight-dependent Generalization of the Binomial Theorem

A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For two special cases of the weight function, i

AN OVERPARTITION ANALOGUE OF THE q-BINOMIAL COEFFICIENTS

We define an overpartition analogue of Gaussian polynomials (also known as q-binomial coefficients) as a generating function for the number of overpartitions fitting inside the M ×N rectangle. We call these new polynomials over Gaussian polynomials or over q-binomial coefficients