Summary
Some inequalities involving the zeros of the classical orthogonal polynomials are established; these are applied to show that certain Riemann sums have monotone convergence.
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References
A. E. Danese,Some inequalities involving Hermite polynomials, American Mathematical Monthly, 64, No. 5 (1957), 344–346.
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P. Turàn,On the zeros of the polynomials of Legendre, Časopis pro pěstováni Matematiky a Fysiky, 75 (1950), 113–122.
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Danese, A.E. Some properties of the zeros of orthogonal polynomials. Annali di Matematica 74, 75–82 (1966). https://doi.org/10.1007/BF02416450
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DOI: https://doi.org/10.1007/BF02416450