A simplification of Ap\'ery's proof of the irrationality of \zeta(3)

TL;DR

This paper presents a simplified proof of the irrationality of  by using 2D recurrence relations and connects these constructions to Ramanujan's continued fraction, making the proof more accessible.

Contribution

It introduces a simplified approach to Ape9ry's proof using 2D recurrence relations and links it to Ramanujan's continued fraction, enhancing understanding.

Findings

Simplified proof of 's irrationality

Connection between recurrence relations and Ramanujan's continued fraction

Clarification of the construction's motivation

Abstract

A simplification of Ap\'ery's proof of the irrationality of \zeta(3) is presented. The construction of approximations is motivated from the viewpoint of 2-dimensional recurrence relations which simplifies many of the details of the proof. Conclusive evidence is also presented that these constructions arise from a continued fraction due to Ramanujan.