Reduction-Based Creative Telescoping for Fuchsian D-finite Functions

TL;DR

This paper introduces a reduction-based creative telescoping algorithm tailored for Fuchsian D-finite functions, extending previous methods for algebraic functions to a broader class of functions.

Contribution

It adapts Trager's Hermite reduction to Fuchsian D-finite functions and generalizes existing algorithms for algebraic functions.

Findings

Developed a new reduction-based algorithm for Fuchsian D-finite functions.

Extended the applicability of creative telescoping techniques.

Unified approach for algebraic and D-finite functions.

Abstract

Continuing a series of articles in the past few years on creative telescoping using reductions, we adapt Trager's Hermite reduction for algebraic functions to fuchsian D-finite functions and develop a reduction-based creative telescoping algorithm for this class of functions, thereby generalizing our recent reduction-based algorithm for algebraic functions, presented at ISSAC 2016.