Related papers: A simple approach to q-Chebyshev polynomials
In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.
In this paper, we derive some new and interesting idebtities for Bernoulli, Euler and Hermite polynomials associated with Chebyshev polynomials.
A tutorial introduction is given to q-special functions and to q-analogues of the classical orthogonal polynomials, up to the level of Askey-Wilson polynomials.
We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.
We give an easy approach to L. Slater's Bailey pairs A(1)-A(8) with the help of q-Lucas polynomials.
Based on a variant of Sury's polynomial identity we derive new expressions for various finite Fibonacci (Lucas) sums. We extend the results to Fibonacci and Chebyshev polynomials, and also to Horadam sequences. In addition to deriving sum…
The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this paper we derive new properties of the Faber--Walsh…
We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in…
We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any…
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 note I collect some typical examples of orthogonal polynomials with simple moments where both moments and orthogonal polynomials have nice q-analogs.
In this paper we derive some new identities involving the Fibonacci and Lucas polynomials and the Chebyshev polynomials of the first and the second kind. Our starting point is a finite trigonometric sum which equals the resolvent kernel on…
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.
The paper contains a generalization of known properties of Chebyshev polynomials of the second kind in one variable to polynomials of $n$ variables based on the root lattices of compact simple Lie groups $G$ of any type and of rank $n$. The…
We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.
Descent polynomials and peak polynomials, which enumerate permutations with given descent and peak sets respectively, have recently received considerable attention. We give several formulas for $q$-analogs of these polynomials which refine…
We give an elementary account of generalized Fibonacci and Lucas polynomials whose moments are Narayana polynomials of type A and type B.
One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q^f(v) for some linear form f. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials,…
The main result of the article says that the formal power series equal to the ratio of two neighboring Chebyshev polynomials, after some renormalization, approximates the generating function of the Catalan numbers. We present a proof of…