In this paper, we consider an approach based on the elementary matrix theory. other words, take into account generalized Gaussian Fibonacci numbers. context, a general tridiagonal family. Then, obtain determinants of family via Chebyshev polynomials. Moreover, one type matrix, whose are Horadam hybrid polynomials, i.e., most form its by means polynomials second kind. We provided several illustr...

Laurent polynomials related to the Hahn-Exton q-Bessel function, which are qanalogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurent q-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orth...

In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous al...

We say that a monic polynomial with integer coefficients is polygomial if its each zero obtained by squaring the edge or diagonal of regular n-gon unit circumradius. find connections certain polygomials Morgan-Voyce polynomials and further Chebyshev second kind.

We construct an Alexander-type invariant for oriented doodles from a deformation of the Tits representation twin group and Chebyshev polynomials second kind. Like Alexander polynomial, our vanishes on unlinked with more than one component. also include values several doodles.

The paper shows that in the analysis of a queuing system with fixed-size batch arrivals, there emerges a set of polynomials which are a generalization of Chebyshev polynomials of the second kind. The paper uses these polynomials in assessing the transient behaviour of the overflow (equivalently call blocking) probability in the system. A key figure to note is the proportion of the overflow (or ...

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 second kind as the special case of the simple group of type A1. The obtained not Laurent-type polynomials are equivalent to the partial cases of theMacdonald symmet...

We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers are suitable for creating a Diffie-Hellman-like key exchange algorithm that is able to withstand attacks using quantum computers. The algorithm takes advantage of the commutative properties of Chebyshev polynomials of the first kind. We show how T polynomial values can be computed faster and how the underlyi...