THE ALI-ABEL THEOREM AND ITS APPLICATION A PREPRINT

Summation by parts formula is a widely used technique in mathematical analysis for computing or evaluating the sums of a given sequence, series or integral that may be otherwise difficult to solve or derive. This formula enables us to simplify complex mathematical expressions by breaking them down into simpler parts, thereby making them more manageable and easy to solve. The basic idea of summation by parts is to express the original expression as a product of two simpler expressions and then apply integration by parts to one of them. This technique has a wide range of applications in various fields such as physics, engineering, statistics, and probability theory, among others. In this article, we will explore the fundamentals of summation by parts formula and its various applications in different fields of mathematics.