Abstract
This paper gives the degree of approximation of function of bounded variation by the partial sums of conjngate Legendre—Fourier Series.
Similar content being viewed by others
References
Bojanic, R. and Vuilleumier, M., On the Rate of Convergence of Fourier—Legerdre Series of Functions of Bounded Variation, J. A. T. 31(1981), 67–79.
Pollard, H., The mean convergence of Orthogonal series I, Trans. A. M. S. 62 (1947), 387–803.
Xie, T. F., Approximation of Legrange Interpolation Polynomial on the basis of the Zeros of Jacobi Polynomial, (to appear).
Xie, T. F., On convergence of Pal—Type interpolation polynomials, Chinese Ann. Math., 9B: 3 (1988), 315–321.
Zhang, P. X., On Conjugate Fourier—Legendre Series, J. Math. Research Exposition, Vol. B, 4 (1993), 365–371.
Szego, G. Orthogonal polynomials, Amer. Math. Soc. Coll. Publ., New York, 1939.
Prinalow, I. I., Randeigenschaften analytischer Funktionen, Deutscher Verlagder Wissensch after, Berlin, 1956.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guohua, Y. On the rate of convergence of conjugate Legendre—Fourier Series of function of bounded variation. Approx. Theory & its Appl. 13, 42–55 (1997). https://doi.org/10.1007/BF02836809
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02836809