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On the Uniform Approximation of Smooth Functions by Jacobi Polynomials

Published online by Cambridge University Press:  20 November 2018

J. Prasad  and
H. Hayashi
J. Prasad
Affiliation:
City University of New York, New York, New York
H. Hayashi
Affiliation:
California State University, Los Angeles, California
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Let ωn(x) denote the Jacobi polynomials with the weight Function

If we denote the corresponding normalized Jacobi polynomials by we Have

(1.1)

Now let

be the nth partial sum of the Fourier series of Jacobi polynomials of a function f(x).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 216 - 223
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Natanson, I. P., Constructive function theory (English transl.), (FUPC, New York, 1964).Google Scholar
2. Prasad, J., Remarks on a theorem of P. K. Suetin, Czechoslovak Math. J. 21 (1971), 349–354.Google Scholar
3. Saxena, R. B., Expansion of continuous differentiable functions in Fourier Legendre series, Can. J. Math. 19 (1967), 823–827.Google Scholar
4. Suetin, P. K., Representation of continuous and differentiable functions by Fourier series of Legendre polynomials, Soviet Math.Dokl. 5 (1964), 1408–1410.Google Scholar
5. Szego, G., Orthogonal polynomials (Amer. Math. Soc. Colloq. Pub. 2nd ed., 1959).Google Scholar