On p. 20 of an [article](https://www.sciencedirect.com/science/article/pii/S0377042700003368?via%3Dihub) by Borwein et al., it is stated that Ramanujan could generalize the following formula due to Glaisher $$\gamma = 2 - 2\log2 -2\sum\_{n=3, \text{ odd}} \frac{\zeta(n)-1}{n(n+1)} $$ to infinitely many formulae for $\gamma$. They refer to Section 19 of Ramanujan's collected papers (which I don't have in my possession). 


I wonder what this collection of series representations for $\gamma$ is, and whether it can be found in another (open-source) reference -- preferably including a derivation. 



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


![](https://ilorentz.org/beenakker/MO/Ramanujan_1917.png)


