Complex Analysis

Mellin-Barnes (MB) integrals are defined in the complex plane as contour integrals over integrands involving the exponential and gamma functions in their most elementary form. Thus we consider basic features of the complex exponential, logarithm, gamma, polygamma, and hypergeometric functions as well as certain generalizations of these functions that appear in particle physics applications. We also discuss general complex integrals and the notion of residues, along with Cauchy’s theorem, and introduce the notion of MB representations. We recall the basic notions and constructions of complex analysis to the level which allows to study the structure and solutions of MB integrals.