Identities inspired by the Ramanujan Notebooks, second series

TL;DR

This paper presents new conjectural formulas inspired by Ramanujan's notebooks, including identities for pi, Catalan's constant, Eisenstein series, and a novel method for computing p(n), based on experimental discovery.

Contribution

It introduces new conjectural identities related to Ramanujan's work, including formulas for pi, Catalan's constant, Eisenstein series, and a novel computational method for p(n).

Findings

New formulas for pi and Catalan's constant.

Identities for Eisenstein series.

A new method for computing p(n).

Abstract

A series of formula is presented that are all inspired by the Ramanujan Notebooks [6]. One of them appears in the notebooks II about Zeta(3). That formula inspired others that appeared in 1998, 2006 and 2009 on the author's website and later in literature [1][2][3]. New formulas for {\pi} and the Catalan constant are presented and a surprising series of approximations. A new set of identities is given for Eisenstein series. All of the formulas are conjectural since they were found experimentally. A new method for the computation of p(n) is presented.