Hermite Reduction for D-finite Functions via Integral Bases

TL;DR

This paper extends Hermite reduction, originally for algebraic functions, to all D-finite functions using integral bases, removing previous restrictions and broadening applicability.

Contribution

It introduces a generalized Hermite reduction algorithm for D-finite functions that works beyond the Fuchsian case, using integral bases.

Findings

The new algorithm applies to arbitrary D-finite functions.

It removes the Fuchsian restriction present in previous methods.

The approach broadens the scope of Hermite reduction techniques.

Abstract

Trager's Hermite reduction solves the integration problem for algebraic functions via integral bases. A generalization of this algorithm to D-finite functions has so far been limited to the Fuchsian case. In the present paper, we remove this restriction and propose a reduction algorithm based on integral bases that is applicable to arbitrary D-finite functions.