## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On a method of approximation by Jacobi polynomials

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 5 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1133793343

Digital Object Identifier
doi:10.36045/bbms/1133793343

Mathematical Reviews number (MathSciNet)
MR2205999

Zentralblatt MATH identifier
1131.33302

#### Citation

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