The art of algorithmic guessing in $\texttt{gfun}$

TL;DR

This paper explores the capabilities of the Maple package gfun for algorithmic guessing of sequences, demonstrating its practical utility through recent mathematical research examples.

Contribution

It provides an in-depth explanation of gfun's features and illustrates their application in current mathematical problems.

Findings

gfun effectively automates sequence guessing in practice

The paper demonstrates gfun's utility with recent research examples

gfun enhances the efficiency of sequence analysis in mathematical research

Abstract

The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the package named $\texttt{gfun}$ in the software Maple. In this text we explore and explain some of $\texttt{gfun}$'s possibilities and illustrate them on two examples from recent mathematical research by the author and his collaborators.