Related papers: A simple approach to q-Chebyshev polynomials

Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play…

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.

In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.

We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…

This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application…

The q-binomial coefficients are the polynomial cousins of the traditional binomial coefficients, and a number of identities for binomial coefficients can be translated into this polynomial setting. For instance, the familiar vanishing of…

A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.

After a short survey about Schroeder numbers and some generalizations which I call Schroeder-like numbers I study some q-analogues which have simple Hankel determinants.

We prove a Lucas-type congruence for q-Delannoy numbers.

A new recursion in only one variable allows very simple verifications of Bressoud's polynomial identities, which lead to the Rogers-Ramanujan identities. This approach might be compared with an earlier approach due to Chapman. Applying the…

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials…

The Rogers-Szeg\"o polynomials are natural q-analogues of Newton binomials. In general they have no closed expression. We consider some exceptional cases which are products of a factor with a closed formula and another one with nice values…

We evaluate various binomial sums involving the powers of Fibonacci and Lucas numbers.

We give simple proofs for the Hankel determinants of q-exponential polynomials.

We study sums of Dirichlet characters over polynomials in $\mathbb{F}_q[t]$ with a prescribed number of irreducible factors. Our main results are explicit formulae for these sums in terms of zeros of Dirichlet L-functions. We also exhibit…

We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we…

In this paper, we investigated properties of Tribonacci-Lucas polynomials which generalized Tribonacci-Lucas numbers. From this generalization, we also obtain some new algebraic properties on these numbers and polynomials as Binet formula,…