Related papers: A note on generalized $q$-difference equations for…
In the first part of the paper we give a definition of G_q-function and we establish a regularity result, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, \S 13]. In the second…
We study $q$-deformed random unitary ensembles associated with the weight function of the Al-Salam--Carlitz orthogonal polynomials, indexed by a parameter $a < 0$. In the special case $a = -1$, the model reduces to the $q$-deformed Gaussian…
An identity involving basic Bessel functions and Al-Salam--Chihara polynomials is proved for which we recover Graf's addition formula for the Bessel function as the base $q$ tends to $1$. The corresponding product formula is derived. Some…
In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…
In this paper, we first construct the homogeneous $q$-shift operator $\widetilde{E}(a,b;D_{q})$ and the homogeneous $q$-difference operator $\widetilde{L}(a,b; \theta_{xy})$. We then apply these operators in order to represent and…
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…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
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 give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning…
We show the polynomial property of $F$-polynomials for generalized quantum cluster algebras and obtain the associated separation formulas under a mild condition. Along the way, we obtain Gupta's formulas of $F$-polynomials for generalized…
This paper presents a new formula for the q-shift operator, building on the techniques by Liu and Sears. This formula provides fresh proof of the Carlitz formula and extends it naturally. As applications, we derive an equivalent form of the…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
In this paper, we obtain affine analogues of Gindikin-Karpelevich formula and Casselman-Shalika formula as sums over Kashiwara-Lusztig's canonical bases. Suggested by these formulas, we define natural $q$-deformation of arithmetical…
In this paper, we give p-adic q-integral representation for the Kim's q-Bernstein polynomials and we give some interesting formulae realted to Carlitz's q-Bernoulli numbers.
In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.
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.
Earlier work introduced a method for obtaining indefinite $q$-integrals of $q$-special functions from the second-order linear $q$-difference equations that define them. In this paper, we reformulate the method in terms of $q$-Riccati…
In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the…