Abstract
AbstractWe consider some perturbations of Chebyshev polynomials of the second kind obtained by modifying by dilation one of its recurrence coefficients at an arbitrary order. By applying Brauer and Geršgorin theorems to Jacobi matrices associated with such perturbed sequences we obtain some locations of their zeros.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Brauer, A.: Limits for the characteristic roots of a matrix. II. Duke Math. J. 14, 21–26 (1947)
2. Castillo, K., Marcellán, F., Rivero, J.: On co-polynomials on the real line. J. Math. Anal. Appl. 427(1), 469–483 (2015)
3. Castillo, K.: Monotonicity of zeros for a class of polynomials including hypergeometric polynomials. Appl. Math. Comput. 266, 183–193 (2015)
4. Chihara, T.S.: An Introduction to Orthogonal Polynomials, Mathematics and its Applications, vol. 13. Gordon and Breach Science Publishers, New York-London-Paris (1978)
5. da Rocha, Z.: A general method for deriving some semi-classical properties of perturbed second degree forms: the case of the Chebyshev form of second kind. J. Comput. Appl. Math. 296, 677–689 (2016)