Dimitrov, D. K.2014-05-202014-05-202001-08-01Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 133, n. 1-2, p. 331-340, 2001.0377-0427http://hdl.handle.net/11449/21710We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.331-340engconnection coefficientszeros of orthogonal polynomialsDescartes' rule of signsWronskiansinequalities for zerosArtigo10.1016/S0377-0427(00)00653-1WOS:000170613700027Acesso abertoWOS000170613700027.pdf1681267716971253