Related papers: A $q$-Umbral Approach to $q$-Appell Polynomials
In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
The $(q,r)$-Whitney numbers were recently defined in terms of the $q$-Boson operators, and several combinatorial properties which appear to be $q$-analogues of similar properties were studied. In this paper, we obtain elementary and…
The main purpose of this paper is to provide a novel approach to deriving formulas for the p-adic q-integral including the Volkenborn integral and the p-adic fermionic integral. By applying integral equations and these integral formulas to…
In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.
Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contained approach to some bivariate analogs.
In this paper, we give a generating function for Multiple Charlier polynomials and deduce several consequences for these polynomials as invertion formula, connection formula, addition formula and recurrences relations they satisfy. Next, we…
In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we…
The present paper deals with multiplication formulas for the Apostol-Genocchi polynomials of higher order and deduces some explicit recursive formulas. Some earlier results of Carlitz and Howard in terms of Genocchi numbers can be deduced.…
The purpose this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta function which interpolates multiple q-Euler numbers at negative integers.
We obtain new explicit formulas for the recurrence coefficients of the q-orthogonal polynomial sequences in a class that extends the q-Askey scheme. Our formulas express the recurrence coefficients in terms of four parameters that determine…
We develop an analog of the exponential families of Wilf in which the label sets are finite dimensional vector spaces over a finite field rather than finite sets of positive integers. The essential features of exponential families are…
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
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.
The aim of this paper is the study of $q^{-1}$-Fibonacci polynomials with $0<q<1$. First, the $q^{-1}$-Fibonacci polynomials are related to a $q$-exponential function which allows an asymptotic analysis to be worked out. Second, related…
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.