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L m Extemal Polynomials Associated with Generalized Jacobi Weights

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Abstract

Asymptotic estimations of the Christoffel type functions for L m extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros of the L m extremal polynomials and the Cotes numbers of the corresponding Turán quadrature formula is given.

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Author notes

  1. Ying-guang Shi

    Present address: Institute of Computational Mathematics & Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 2719, Beijing, 100080, China

Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    Ying-guang Shi

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  1. Ying-guang Shi
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Correspondence to Ying-guang Shi.

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Supported by the National Natural Science Foundation of China (No. 19971089).

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Shi, Yg. L m Extemal Polynomials Associated with Generalized Jacobi Weights. Acta Mathematicae Applicatae Sinica, English Series 19, 205–218 (2003). https://doi.org/10.1007/s10255-003-0096-0

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  • DOI: https://doi.org/10.1007/s10255-003-0096-0

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