On a pair of Ramanujan’s modular equations and P -Q theta functions of level 35

Abstract

S. Ramanujan recorded several modular equations and P -Q theta function identities in his notebooks andlost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equationsand two P -Q theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modularforms.