An analysis on fourier series expansion

Abstract

The present paper is involved with the analyze of Fourier coefficients with help of extension of Gauss partial sum for Fourier series. The Fourier series are specific and standard series of periodic functions which are discussed in varies area of applied mathematics. The discussed functions have period Q in which they are piecewise continuously and uniform on said period. By study on extension of the Fourier series sum on periodic functions, we are able to extend Gauss partial sum.