Transcendence Certificates for D-finite Functions

TL;DR

This paper introduces a new sufficient condition for certifying the transcendence of D-finite functions, addressing practical challenges where existing methods are inconclusive.

Contribution

It proposes an additional transcendence criterion that improves the ability to certify transcendence in cases where previous tests fail.

Findings

New condition detects transcendence in previously unresolved cases

Enhances practical transcendence certification methods

Addresses limitations of existing tests

Abstract

Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we propose an additional such condition which catches some cases on which other tests fail.