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Orthogonal polynomials satisfy a recurrence relation of order two, whereappear two coefficients. If we modify one of these coefficients at a certainorder, we obtain a perturbed orthogonal sequence. In this work we consider inthis way some perturbed of Chebyshev polynomials of second kind and we dealwith the problem of finding the connection coefficients that allow to write theperturbed sequence in terms of the original one and in terms of the canonicalbasis. From the connection relations obtained and from two other relations, wededuce some results about zeros and interception points of these perturbedpolynomials. All the work is valid for arbitrary order of perturbation.

On connection coefficients, zeros and interception points of some perturbed of arbitrary order of the Chebyshev polynomials of second kind