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

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 $1\mathrm{/}\pi$ associated with the classical, cubic and quartic bases.