Related papers: A New Formula of q-Fubini Numbers via Goncharov po…
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…
The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find…
Classical Gon\v{c}arov polynomials are polynomials which interpolate derivatives. Delta Gon\v{c}arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental…
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are…
In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…
In connection with cluster algebras, snake graphs and q-integers, Kyungyong Lee and Ralf Schiffler recently found a formula for computing the (normalized) Jones polynomials of rational links in terms of continued fraction expansion of…
We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal…
The main purpose of this paper is to introduce and investigate a new class of generalized Genocchi polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pint\'er addition…
In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results new explicit formulas for p-Bernoulli numbers and…
In 2013, Pak and Panova proved the strict unimodality property of $q$-binomial coefficients $\binom{\ell+m}{m}_q$ (as polynomials in $q$) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients.…
In 1920, MacMahon introduced two families of $q$-series to study divisor sums. Recent work has shown that MacMahon's $q$-series are closely connected to overpartitions and $3$-colored partitions. Merca introduced truncated forms of…
Remixed Eulerian numbers are a polynomial $q$-deformation of Postnikov's mixed Eulerian numbers. They arose naturally in previous work by the authors concerning the permutahedral variety and subsume well-known families of polynomials such…
We determine all permutation polynomials among several families of polynomials over $\mathbb{F}_{q^3}$ for arbitrary prime powers $q$. We obtain some new families of permutation polynomials over $\mathbb{F}_{q^3}$ with simple coefficients…
In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator. Also, we show between the q-Euler…
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a…
In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.
In the present paper, we propose the modified q-Bernstein polynomials of degree n, which are different q-Bernstein polynomials of Phillips(see [4]). From these the modified q-Bernstein polynomials of degree n, we derive some interesting…
The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. we unify all forms of q-exponential functions by one more parameter. we…
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…