Related papers: A simple approach to q-Chebyshev polynomials
This overview article gives an elementary approach to continuous q-Hermite polynomials. We stress their relation to Fibonacci, Lucas and Chebyshev polynomials and to some q-analogues of these polynomials.
We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.
Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contained approach to some bivariate analogs.
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
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.
The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers…
We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.
In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.
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…
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.
Using generating functions, we derive many identities involving balancing and Lucas-balancing polynomials. By relating these polynomials to Chebyshev polynomials of the first and second kind, and Fibonacci and Lucas numbers, we offer some…
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…
In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci…
Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…
We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.