Interlacing properties of zeros of multiple orthogonal polynomials

Details Interlacing properties of zeros of multiple orthogonal polynomials Interlacing properties of zeros of multiple orthogonal polynomials

2011-08-19

arxiv.org/abs/1108.3917v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

It is well known that the zeros of orthogonal polynomials interlace. In this paper we study the case of multiple orthogonal polynomials. We recall known results and some recursion relations for multiple orthogonal polynomials. Our main result gives a sufficient condition, based on the coefficients in the recurrence relations, for the interlacing of the zeros of neighboring multiple orthogonal polynomials. We give several examples illustrating our result.

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