Summations of Linear Recurrent Sequences

TL;DR

This paper extends Sister Celine's method for proving hypergeometric sum identities, enabling it to handle more complex summands and applying it to derive new results and reprove known ones automatically.

Contribution

The paper introduces an extended method for hypergeometric sum identities that broadens the class of summands it can handle, facilitating automated proofs and new discoveries.

Findings

New identities proved automatically

Reproving known results efficiently

Extended method handles more complex summands

Abstract

We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already known results in an automated way.