# Integral Recurrences from A to Z

## By Robert Dougherty-Bliss

## View

Appeared in *The American Mathematical Monthly (circa 2022)*

George Boros and Victor Moll’s masterpiece *Irresistible Integrals* does well
to include a suitably-titled appendix, “The Revolutionary WZ Method,” which
gives a brief overview of the celebrated Wilf-Zeilberger method of definite
summation. Paradoxically, *Irresistible Integrals* does not contain the
suitably-titled appendix, “The Revolutionary AZ Method,” which would have been
an excellent place to give a brief overview of the Almkvist-Zeilberger method
of definite *integration*! This omission can be forgiven, but once realized it
must be rectified. The remarkable AZ machinery deserves to be more widely known
to the general public than it is. We will do our part by presenting a series of
case studies that culminate in a - fun but overkill - integral-based proof that
e is irrational.