Wronskians of theta functions and series for $1/\pi$

TL;DR

This paper introduces new functions similar to Ramanujan's, used to analyze series for 1/π related to classical, cubic, and quartic bases, enhancing understanding of these mathematical series.

Contribution

It defines new functions analogous to Ramanujan's and applies them to study series for 1/π across different bases, providing novel insights.

Findings

New functions analogous to Ramanujan's $f(n)$ are defined.

These functions are used to analyze series for 1/π.

Results connect classical, cubic, and quartic bases in Ramanujan's series.

Abstract

In this article, we define functions analogous to Ramanujan's function $f(n)$ defined in his famous paper "Modular equations and approximations to $\pi$". We then use these new functions to study Ramanujan's series for $1/\pi$ associated with the classical, cubic and quartic bases.