The three missing terms in Ramanujan’s septic theta function identity

Abstract On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for theta function $$\varphi (q)$$ φ ( q ) : $$\begin{aligned} \varphi (e^{-7\pi \sqrt{7}}) = 7^{-3/4}\varphi (e^{-\pi \sqrt{7}})\big \{1 + (\quad )^{2/7} )^{2/7}\big \}. \end{aligned}$$ e - 7 π = 3 / 4 { 1 + 2 } . We give three missing terms. In addition, we calculate class invariant $$G_{343}$$ G 343 and further special values of (e^{-n\pi }),$$ n , $$n 7, 21, 35,$$ 21 35 49.