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.
@article{bwmeta1.element.doi-10_1515_math-2016-0063, author = {Ivan Gonzalez and Lin Jiu and Victor H Moll}, title = {Pochhammer symbol with negative indices. A new rule for the method of brackets}, journal = {Open Mathematics}, volume = {14}, year = {2016}, pages = {681-686}, zbl = {1347.33014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0063} }
Ivan Gonzalez; Lin Jiu; Victor H Moll. Pochhammer symbol with negative indices. A new rule for the method of brackets. Open Mathematics, Tome 14 (2016) pp. 681-686. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0063/