Creative telescoping is the core of Zeilberger's method for computer-generated proofs of identities in combinatorics and special functions.
Since the early 1990s, four classes of algorithms have been developed for creative telescoping. The fourth and most recent one is based on Hermite reduction and its variants.
This idea was first worked out for bivariate rational functions in 2010. It has since been extended to more general classes of functions, such as hyperexponential functions, hypergeometric terms, algebraic functions and most recently D-finite functions.
In this talk, we will explain the idea of this approach and a striking advantage over earlier algorithms.