An Extension of the Method of Brackets: Part 1

Authors

Ivan Gonzalez, Universidad de ValparaisoFollow
Karen T. Kohl, University of Southern MississippiFollow
Lin Jiu, Johannes Kepler UniversityFollow
Victor H. Moll, Tulane UniversityFollow

Document Type

Article

Publication Date

9-27-2018

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n 2 C, but might vanish or blow up when n 2 N. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.

Comments

Published by Open Mathematics at 10.1515/math-2017-0100.

Publication Title

Open Mathematics

Volume

15

Issue

1

First Page

1181

Last Page

1211

Recommended Citation

Gonzalez, I., Kohl, K. T., Jiu, L., Moll, V. H. (2018). An Extension of the Method of Brackets: Part 1. Open Mathematics, 15(1), 1181-1211.
Available at: https://aquila.usm.edu/fac_pubs/15400