We study the regularity of form ( linear functional) satisfying functional equation (x2 ? c2)u = ?v where c C, C {0} and v is perturbed order one Chebyshev second kind. The integral representation u highlighted. Moreover, some symmetric degree forms class two four are given.

with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...

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.

In this paper, we derive a single formula for the entries of the rth (r ∈ N) power of a certain real circulant matrix of odd and even order, in terms of the Chebyshev polynomials of the first and second kind. In addition, we give two Maple 13 procedures along with some numerical examples in order to verify our calculation.

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

A wide area of research has been done in the field of noise removal in Electrocardiogram signals.. Electrocardiograms (ECG) play an important role in diagnosis process and providing information regarding heart diseases. In this paper, we propose a new method for removing the baseline wander interferences, based on discrete wavelet transform and Butterworth/Chebyshev filtering. The ECG data is t...