Here is a scan from Ramanujan's 1917 paper on the generalized $\gamma$ formulas (equations 5 and 7). The reference in <A HREF="https://en.wikipedia.org/wiki/Messenger_of_Mathematics">Messenger of Mathematics</A> is a journal that no longer exists. Only the volumes through 1901 are freely accessible <A HREF="https://gdz.sub.uni-goettingen.de/id/PPN599484047?page=1">online.</A>

<IMG SRC="https://ilorentz.org/beenakker/MO/Ramanujan_1917.png"/>