2002/03/28 by Franz Peherstorfer, Peherstorfer, Franz
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #math-ph #math.CA #math.MP #msc:42c05
paper · pdf · doi:10.48550/arxiv.math-ph/0203058
21pages, revised and extended version, slight corrections also
arxiv created 2002/04/30 · arxiv updated 2009/11/30
First a formula for the number of zeros of the orthogonal polynomial in the intervals is presented. Then a criteria about the appearance of a zero in a gap is given. Finally a necessary and sufficient condition is derived such that the zeros of the orthogonal polynomials have given accumulation points in the gaps. As a consequence it follows that every point from the gaps is an accumulation point of the zeros of the orthogonal polynomials, if the harmonic measures of the intervals are linearly independent over the rationals. If the harmonic measures are rational then there is a finite number of accumulation points only.