Title: An Extension of the Method of Brackets. Part 1,
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 $a_{n}$ have meromorphic representations for $n
\in \mathbb{C}$, but might vanish or blow up when $n \in \mathbb{N}$. These
ideas are illustrated with the evaluation of a variety of entries from the
classical table of integrals by Gradshteyn and Ryzhik.