Related papers: Continuous q-Hermite polynomials: An elementary ap…

In this paper, we get the generating functions of q-Chebyshev polynomials using operator. Also considering explicit formulas of q-Chebyshev polynomials, we give new generalizations of q-Chebyshev polynomials called incomplete q-Chebyshev…

The objective of this paper is to derive some interesting properties of Genocchi, Euler and Bernstein polynomials by means of the orthogonality of Hermite polynomials.

We introduce two classes of $(p,q)$-It\^o--Hermite polynomials, the post-quantum analogs of the $q$-It\^o--Hermite polynomials introduced recently by Ismail and Zhang. We study their basic properties such as their operational formulas of…

Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this…

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.

Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.

A simple matrix formulation of the Fibonacci, Lucas, Chebyshev, and Dixon polynomials polynomials is presented. It utilizes the powers and the symmetric tensor powers of a certain matrix.

This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear…

New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a…

In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.

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…

We give an elementary account of generalized Fibonacci and Lucas polynomials whose moments are Narayana polynomials of type A and type B.

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

Some $q-$analogues of the normal ordering of the operator $(X+sD)^n$ on the polynomials are derived.

This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.

We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.

We introduce bivariate versions of the continuous q-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence…

We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of…

We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the…

In this paper, we consider Hermite and poly-Bernoulli mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities associated with Stirling numbers,…