A Study Of Summability Of Derived ourier Series And Its Conjugate By Matrix Method - Amer, Mohamed Mahmoud (Journal of natural sciences, life and applied sciences, 2019)
There are many types of criteria, under various conditions, for the matrix summation of a derivative Fourier series. Here, we will study an important and distinct type of criteria for the matrix summation of a derivative Fourier series. We will consider the function f(x) to be periodic with a period of 2π and Liebig integrable on the interval [-π, π], and the matrix T = (a_n,k) to be regular. We will prove that the series _n=1^∞nB_n(x) is matrix summation to the sum O(1), which is a bounded function, as we will see later, and that the series -_n=1^∞nA_n(x) is matrix summation to the sum: 14 -14π_0^πh(t).cosec^212tdt+O(1)