Description
We elaborate on the method of parametric annihilators for deriving relations
among integrals. Annihilators are differential operators that annihilate multi-valued
integration kernels appearing in suitable integral representations of special functions and
Feynman integrals. We describe a method for computing parametric annihilators based on
efficient linear solvers and show how to use them to derive relations between a wide class
of special functions. These include hypergeometric functions, Feynman integrals relevant
to high-energy physics and duals of Feynman integrals. We finally present the public
Mathematica package CALICO for computing parametric annihilators and its usage in
several examples and modern applications.