A note on the interlacing of zeros and orthogonality Original Research Article

Let View the MathML source{tn}n=0∞ be a sequence of monic polynomials with deg(tn)=ndeg(tn)=n such that, for each n∈Nn∈N, the zeros of tntn are real and simple and tntn and tn+1tn+1 have no common zeros. We discuss the connection between the orthogonality of the sequence, the positivity of a certain ratio, and the interlacing of the zeros of tntn and tn+1tn+1 for n≥1n≥1, n∈Nn∈N.