A STUDY ON SINGULAR POINT/SINGULARITY OF COMPLEX ANALYSIS

Abstract

To study the Points at which a function f(z) is not analytic are called singular points or singularities of f(z). To study the different types of singularity of a complex function f(z) are discussed and the definition of a residue at a pole is given. The residue theorem is used to evaluate contour integrals where the only singularities of f(z) inside the contour are poles. The function f(z) has a singularity at z = z0 and in a neighbourhood of z0 (i.e. a region of the complex plane which contains z0) there are no other singularities then z0 is an isolated singularity of f(z).