The method of brackets. Part 2: examples and applications

TL;DR

This paper introduces a heuristic method called the method of brackets for evaluating definite integrals, originating from Feynman diagram techniques, and demonstrates its application through examples.

Contribution

It presents the operational rules of the method of brackets and illustrates its effectiveness in simplifying integral evaluations.

Findings

Reduces integral evaluation to solving linear systems

Applicable to a broad class of definite integrals

Demonstrated through multiple examples

Abstract

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is illustrated with several examples. The method of brackets reduces the evaluation of a large class of definite integrals to the solution of a linear system of equations.