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.
