Bulletin of the Belgian Mathematical Society - Simon Stevin

On a method of approximation by Jacobi polynomials

R.K. Dubey and R.K. Pandey

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Convolution structure for Jacobi series allows end point summability of Fourier-Jacobi expansions to lead an approximation of function by a linear combination of Jacobi polynomials. Thus, using Ces$\grave a$ro summability of some orders $>1$ at $x=1,$ we prove a result of approximation of functions on $[-1,1]$ by operators involving Jacobi polynomials. Precisely, we pick up functions from a Lebesgue integrable space and then study its representation by Jacobi polynomials under different conditions.

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Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 4 (2005), 557-564.

First available in Project Euclid: 5 December 2005

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Dubey, R.K.; Pandey, R.K. On a method of approximation by Jacobi polynomials. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 4, 557--564. doi:10.36045/bbms/1133793343. https://projecteuclid.org/euclid.bbms/1133793343

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