Efficient Algorithms for Mixed Creative Telescoping

TL;DR

This paper introduces an efficient creative telescoping algorithm for mixed continuous-discrete cases, specifically for bivariate hypergeometric-hyperexponential terms, providing minimal-order telescopers with tight size bounds.

Contribution

It presents a novel Hermite-like reduction-based algorithm for mixed creative telescoping, optimizing for efficiency and minimal order in the output.

Findings

The algorithm is efficient for the targeted class of functions.

It produces minimal-order telescopers with tight size bounds.

The approach advances symbolic integration and summation techniques.

Abstract

Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the integration of bivariate hypergeometric-hyperexponential terms. We design a new creative telescoping algorithm operating on this class of inputs, based on a Hermite-like reduction procedure. The new algorithm has two nice features: it is efficient and it delivers, for a suitable representation of the input, a minimal-order telescoper. Its analysis reveals tight bounds on the sizes of the telescoper it produces.