Mellin Transform And Isolated Singularities

Abstract

Mellin Transform is method for the exact calculation of onedimensional definite integrals, and illustrates the application. 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. Every singularity of a holomorphic function is isolated, but isolation of singularities is not alone sufficient to guarantee a function is holomorphic. Many important tools of complex analysis and the residue theorem require that all relevant singularities of the function be isolated.