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Positivity of the cotes numbers for some Jacobi abscissas

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Abstract

Some old quadrature schemes are shown to be positive.

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References

  1. Askey, R., Fitch, J.: Positivity of the Cotes numbers for some ultraspherical abscissas. SIAM J. Numer. Anal.5, 199–201 (1968).

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  3. Fejér, L.: Mechanische Quadraturen mit positiven Cotesschen Zahlen. Math. Z.37, 289–309 (1933).

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  4. Szegö, G.: Asymptotische Entwicklungen der Jacobischen Polynome. Schriften Königsberger Gelehrten Gesellschaft, naturwissenschaftliche Klasse.10, 35–112 (1933).

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  5. Szegö, G.: Orthogonal Polynomials. Amer. Math. Soc. Colloq. Pub. 23, Providence, R. I. (1967).

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Van Vleck Hall, 53706, Madison, Wisconsin, USA

    Richard Askey

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  1. Richard Askey
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Supported in part by N.S.F. grant GP 24182.

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Askey, R. Positivity of the cotes numbers for some Jacobi abscissas. Numer. Math. 19, 46–48 (1972). https://doi.org/10.1007/BF01395928

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  • DOI: https://doi.org/10.1007/BF01395928

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