Pochhammer Symbol with Negative Indices. A New Rule for the Method of Brackets

TL;DR

This paper introduces a new evaluation rule for the method of brackets, a heuristic integration technique, motivated by an example involving Bessel functions, aiming to improve its rigor and applicability.

Contribution

The paper proposes a novel rule for the method of brackets, enhancing its theoretical foundation and potential for evaluating complex integrals.

Findings

New evaluation rule for the method of brackets

Application to integrals involving Bessel functions

Improved rigor in heuristic integration methods

Abstract

The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.