# Polynomial Continued Fractions

## TL;DR

This paper explores polynomial continued fractions with higher degrees in numerator and denominator, extending classical work and analyzing limits that can be rational or irrational.

## Contribution

It introduces new analyses for polynomial continued fractions with higher degrees, especially where numerator and denominator degrees are equal, expanding on Ramanujan's classical results.

## Key findings

- Extended analysis of polynomial continued fractions with higher degrees
- Identified conditions for rational and irrational limits
- Generalized Ramanujan's work on continued fractions

## Abstract

Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher degree for both numerator and denominator polynomials, with particular attention given to cases in which the degrees are equal. We extend work of Ramanujan on continued fractions with rational limits and also consider cases where the limits are irrational.