Summability of Orthogonal Series by Absolute Matrix Method - Alhashemi, Ghina Mohammed Gehad; Amer, Mohammed Mahmoud (Journal of natural sciences, life and applied sciences, 2020)
At the beginning of the 20th century, the theory of perpendicular series orthogonal, which treated sentences of orthogonal functions as a natural generalization of series theory. The perpendicular mass idyllability many methods, such as the Reimann, Norlund, Cesaro, Holder, and generalized Norlund methods, has been studied. In this research, we studied the summability of simple orthogonal series in different methods called absolute methods that rely heavily on differences.This is done by relying on some research, articles and scientific books in the field of summability of series. The absolute matrix methods are one of the most important methods of absolute summability. Most absolute summability methods are special cases of absolute matrix method. We finally recommend a double case study.
Keywords: matrix method; absolute matrix method; generalized Newerland method; generalized absolute Newerland method; orthogonal series; summation