相关论文: Moments of q-Jacobi Polynomials and q-Zeta Values
By the symmetric properties of Drichlet's type multiple q-l-function, we establish various identities concerning the generalized higher-order q-Euler polynomials. Furthermore, we give some interesting relationship between the power sums and…
We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\chi_d)$, and also of the $L$-functions associated to quadratic twists of an…
We study special values for the continuous $q$-Jacobi polynomials and present applications of these special values which arise from bilinear generating functions, and in particular the Poisson kernel for these polynomials.
In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers…
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…
Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
In this paper, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally,…
We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating…
In this research, as the new results of our previously proposed definition for the new class of $2D$ $q$-Appell polynomials, we derive some interesting relations including the recurrence relation and partial $q$-difference equation of the…
In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.
A well-known result, due to Dirichlet and later generalized by de la Vallee-Poussin, expresses a relationship between the sum of fractional parts and the Euler-Mascheroni constant. In this paper, we prove an asymptotic relationship between…
Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…
One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
In this paper, we present some criteria for the $2$-$q$-log-convexity and $3$-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of certain infinite triangular array $[A_{n,k}(q)]_{n,k\geq0}$ of…
In this paper we study (h,q)-zeta functions associated with (h,q)-Bernoulli numbers and polynomials.
We investigate the interlacing of zeros of polynomials of different degrees within the sequences of $q$-Laguerre polynomials $\left\{\tilde{L}_n^{(\delta)}(z;q)\right\}_{n=0}^{\infty}$ characterized by $\delta\in(-2,-1).$ The interlacing of…
In this paper, we focus on the q-Genocchi numbers and polynomials. We shall introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integral on Zp which are very important in the study of…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…