Creative Telescoping for Holonomic Functions

TL;DR

This paper provides an accessible introduction and survey of creative telescoping, illustrating its practical applications and summarizing two decades of developments in the study of holonomic functions.

Contribution

It offers a practical overview of creative telescoping techniques and surveys significant progress and applications over the past twenty years.

Findings

Demonstrates practical applications of creative telescoping

Summarizes two decades of research developments

Highlights the impact across various mathematical contexts

Abstract

The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified. On the other hand, this chapter has the flavour of a survey article: the developments in this area during the last two decades are sketched and a selection of references is compiled in order to highlight the impact of creative telescoping in numerous contexts.