Marcellán Español, Francisco JoséPetronilho, José2009-12-212009-12-212000Communications in the Analytic Theory of Continued Fractions, 2000, n. 8, p. 88-116https://hdl.handle.net/10016/618129 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1789676 (2001m:42047)We present characterization theorems for orthogonal polynomials obtained from a given system of orthogonal polynomials by a cubic polynomial transformation in the variable. Since such polynomials are the denominators of the approximants for the expansion in continued fractions of the x-transform of the moment sequences associated with the linear functionals with respect to which such polynomials are orthogonal, we state the explicit relation for the corresponding formal Stieltjes series. As an application, we study the eigenvalues of a tridiagonal 3-Toeplitz matrix. Finally, we deduce the second-order linear differential equation satisfied by the new family of orthogonal polynomials when the initial family satisfies such a kind of differential equation.application/pdfeng© Mesa State CollegeOrthogonal polynomialsPolynomial mappingsRecurrence coefficientsStieltjes formal seriesToeplitz matricesSieved orthogonal polynomialsresearch articleMatemáticasopen access