Rate of convergence of Fourier–Legendre series of functions of the class (n^α)BV^p [−1, 1]

Abstract

In this paper, the rate of convergence of the Fourier–Legendre series of functions of the class (n^α)BV^p[−1, 1] and in particular, the class BV^p[−1, 1], are estimated. The result obtained is a similar to a result of Bojani´c and Vuilleumier for the Fourier–Legendre series of functions of bounded variation, and is applicable to wider class.