Mellin-Barnes and the method of brackets

TL;DR

This paper introduces a novel application of the method of brackets to evaluate Mellin-Barnes integrals by transforming them into bracket series, demonstrating its effectiveness through various examples.

Contribution

It presents a new approach for evaluating Mellin-Barnes integrals using the method of brackets, expanding the gamma function in series form.

Findings

Effective evaluation of Mellin-Barnes integrals demonstrated

Method shows flexibility across different examples

Gamma function expansion is central to the approach

Abstract

The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral representations into a bracket series to obtain their values. The expansion of the gamma function in such a series constitute the main part of this new application. The power and flexibility of this procedure is illustrated with a variety of examples.