On Euler polynomial continued fractions

TL;DR

This paper introduces polynomial continued fractions, focusing on Euler continued fractions, and presents an algorithm for their identification, highlighting their interesting patterns despite some differences from simple continued fractions.

Contribution

The paper develops the concept of polynomial continued fractions and provides an algorithm specifically for identifying Euler continued fractions within this framework.

Findings

Polynomial continued fractions exhibit interesting exploitable patterns.

An algorithm for identifying Euler continued fractions is proposed.

These fractions differ from simple continued fractions but share some useful properties.

Abstract

In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing properties of simple continued fractions, polynomial continued fractions have many interesting patterns which can be exploited. Specifically, we explore the Euler continued fractions within this framework and present an algorithm for their identification