P-finite Recurrences From Generating Functions with Roots of Polynomials

TL;DR

This paper develops methods to derive P-finite recurrences for sequences with generating functions involving polynomial roots, focusing on establishing D-finite differential equations to facilitate series reduction.

Contribution

It introduces a systematic approach to obtain P-finite recurrences from generating functions with roots of polynomials, expanding the toolkit for analyzing such sequences.

Findings

Derived P-finite recurrences for specific classes of sequences

Established D-finite differential equations for generating functions

Facilitated reduction of power series expansions

Abstract

We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their power series expansions apply.