Related papers: A commuting q-analogue of the addition formula for…
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously known addition formulas for $q$-Legendre…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
Let the symmetric functions be defined for the pair of integers $\left( n,r\right) $, $n\geq r\geq 1$, by $p_{n}^{\left( r\right) }=\sum m_{\lambda }$ where $m_{\lambda }$ are the monomial symmetric functions, the sum being over the…
The theory of q-analogs develops many combinatorial formulas for finite vector spaces over a finite field with q elements--all in analogy with formulas for finite sets (which are the special case of q=1). A direct-sum decomposition of a…
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…
Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beautiful expansion formula which can be viewed as a…
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 a…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
This work presents a new interpolation tool, namely, cubic $q$-spline. Our new analogue generalizes a well known classical cubic spline. This analogue, based on the Jackson $q$-derivative, replaces an interpolating piecewise cubic…
We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.
We give formulas for the products of classes of Schubert varieties in the quantum cohomology rings of Grassmannians, in terms of the combinatorics of partitions and tableaux.
We give a $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: {align*} \sum_{k=0}^{\lfloor n/2\rfloor}{m+k\brack k}_{q^2}{m+1\brack n-2k}_{q} q^{n-2k\choose 2} &={m+n\brack…
In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to…
In this paper, we introduce a new analogue of Lorentz polynomials based on (p,q)-integers and we call it as (p,q)-Lorentz polynomials. We obtain quantitative estimate in the Voronovskaja's type thoerem and exact orders in simultaneous…
In this paper, we investigate a specific class of $q$-polynomial sequences that serve as a $q$-analogue of the classical Appell sequences. This framework offers an elegant approach to revisiting classical results by Carlitz and, more…
We construct discrete analogues of the Dixmier operators, that is, commuting difference operators corresponding to a spectral curve of genus 1 whose coefficients are polynomials of the discrete variable.
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
We present an asymmetric $q$-Painlev\'e equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlev\'e equation (up to a simple…