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Some properties of the zeros of orthogonal polynomials

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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.

References

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    A. E. Danese,Some inequalities involving Hermite polynomials, American Mathematical Monthly, 64, No. 5 (1957), 344–346.

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    G. Szegö,Orthogonal Polynomials, American Mathematical Society, New York, 1959.

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    G. Szegö andP. Turan,On the monotone convergence of certain Riemann sums, Publicationes Mathematicae, Debrecen, 8 (1961), 326–335.

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    K. Venkatachaliengar andS. K. Lakshmana Rao,On Turán's inequality for ultra-spherical polynomials, Proceedings of the American Mathematical Society, 8, No. 6 (1957), 1075–1087.

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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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Keywords

  • Orthogonal Polynomial
  • Monotone Convergence
  • Classical Orthogonal Polynomial