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An asymptotic expansion formula of kernel function for Quasi Fourier-Legendre series and its application

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Approximation Theory and its Applications

Abstract

Is this paper we shall give an asymptotic expansion formula of the kernel function for the Quasi Fourier-Legendre series on an ellipse, whose error is O(1/n2) and then applying it we shall show an analogue of an exact result in trigonometric series.

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References

  1. Szegö, G., Orthogonal Polynomials, Amer. Math. Soc. Colloq Publ. 23, 1939.

  2. Zhang Peixuan, The Lebesgue Constants of the Biorthonormal System {P n, Qn} and “Jackson” Type Theorem for a Kind of New Approximation Problem, Approx. Theory & its Appl., 6:3(1990) 102–113.

    MathSciNet  MATH  Google Scholar 

  3. Natanson, I.P., Konstructive Funktionentheorie, Akadademie-Verlag, Berlin, 1955.

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  4. Elliott, D., Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function, Math. comp., V25, No. 114, (1971) 309–315.

    Article  MathSciNet  Google Scholar 

  5. Zygmud, A., Trigonometric Series, Oxford Univ. Press, 1959.

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Peixuan, Z. An asymptotic expansion formula of kernel function for Quasi Fourier-Legendre series and its application. Approx. Theory & its Appl. 13, 33–42 (1997). https://doi.org/10.1007/BF02836894

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  • DOI: https://doi.org/10.1007/BF02836894

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