Electronic International Standard Serial Number (EISSN)
1879-1778
abstract
Given {P"n}"n">="0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e., Q"n(x)=P"n(x)+a"1P"n"-"1(x)+...+a"kP"n"-"k,a"k<>0,n>k. Necessary and sufficient conditions are given for the orthogonality of the sequence {Q"n}"n">="0. An interesting interpretation in terms of the Jacobi matrices associated with {P"n}"n">="0 and {Q"n}"n">="0 is shown. Moreover, in the case k=2, we characterize the families {P"n}"n">="0 such that the corresponding polynomials {Q"n}"n">="0 are also orthogonal.