Reduction-based Creative Telescoping for P-recursive Sequences via Integral Bases

TL;DR

This paper introduces a novel reduction-based creative telescoping method for P-recursive sequences, utilizing integral bases to efficiently decompose sequences into summable and non-summable parts, enhancing computational approaches.

Contribution

It presents a new algorithm that leverages integral bases for the reduction-based creative telescoping of bivariate P-recursive sequences, improving decomposition accuracy.

Findings

Effective decomposition into summable and non-summable parts

Minimal non-summable parts achieved through the method

Enhanced algorithm performance for P-recursive sequences

Abstract

We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative telescoping algorithm based on the concept of integral bases.