SOME IDENTITIES CONNECTED WITH A CONTINUED FRACTION OF RAMANUJAN

Abstract

We first prove two identities which are analogous to Entry 3.3.4 in Ramanujan's lost notebook. The identities in Entry 3.3.4 come out equal to a cubic theta function of Borwein and Borwein [5]. In our case they come out equal to $\frac{(q^4;q^4)^2}{(q^2;q^4)^2} C^2(q)$. We also express $C(q)$ in terms of theta functions $\phi(q)$ and $\psi(q)$. A series expansion of $\log C(q)$ is also given. One of the identities (9) is equivalent to a Theorem in partitions.