S. Ramanujan recorded several modular equations and $P$-$Q$ theta function identities in his notebooks and lost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equations and two $P$-$Q$ theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modular forms.
VASUKI, K. R. and T, ANUSHA
"On a pair of Ramanujan's modular equations and $P$-$Q$ theta functions of level 35,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/6