Cauchy integral formula - Azram, Mohammad; Elfaki, Faiz Ahmed Mohamed (IOP Publishing, 2013)
Cauchy-Goursat integral theorem is pivotal, fundamentally important, and well celebrated result in complex integral calculus. It requires analyticity of the function inside and on the boundary of the simple closed curve. In this study we will investigate the condition(s) under which integration of f(z) along the close contour C is equal to zero, even though the function is not analytic at a point inside C. Consequently,we will extend the above notion to a finite numbers of points and will present an easy and simple proof of unquestionably the most important, significant and pivotal result known as Cauchy integral formula.