相关论文: An analytical expression for the third coefficient…

We use $q$-binomial theorem to prove three new polynomial identities involving $q$-trinomial coefficients. We then use summation formulas for the $q$-trinomial coefficients to convert our identities into another set of three polynomial…

We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved…

We study three different $q$-analogues of the harmonic numbers. As applications, we present some generating functions involving number theoretical functions and give the $q$-generalization of Gosper's exponential generating function of…

We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of $q$-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\'e equations, in a Lax form,…

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

We apply big data techniques, including exploratory and topological data analysis, to investigate quantum invariants. More precisely, our study explores the Jones polynomial's structural properties and contrasts its behavior under four…

We present an analytical expression for the static many-body local field factor $G_{+}(q)$ of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small…

The purpose of this article is to bring together the third-order Jacobsthal numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and…

The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the…

The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a…

The $q$-analogue of the binomial coefficient, known as a $q$-binomial coefficient, is typically denoted $\left[{n \atop k}\right]_q$. These polynomials are important combinatorial objects, often appearing in generating functions related to…

In this paper, a new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A Vadja formula for the generalized bihyperbolic third-order Jacobsthal…

An addition and product formula for the Hahn-Exton $q$-Bessel function, previously obtained by use of a quantum group theoretic interpretation, are proved analytically. A (formal) limit transition to the Graf addition formula and…

We introduce a family of polynomials in $q^2$ and four variables associated with the quantized algebra of functions $A_q(C_2)$. A new formula is presented for the recent solution of the 3D reflection equation in terms of these polynomials…

Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.

We show an inequality involving the third largest or second smallest dual eigenvalues of $Q$-polynomial association schemes of class at least three. Also we characterize dual-tight $Q$-polynomial association schemes of class three. Our…

We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…

In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we…

The QCD partition function in the external stationary gluomagnetic field is computed in the third order in external field invariants in arbitrary dimension and arbitrary covariant gauge. The contributions proportional to third order…

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…