On some P-Q mixed modular equations of degree 5

Abstract

In his second notebook, Ramanujan recorded total of 23 P-Q modular equations involving theta-functions $f(-q)$, $\phi (q)$ and $\psi (q)$. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving $f(-q)$. As a consequence, values of certain quotients of theta-function are evaluated.