[Posted on december 15, 2016.]
Having for a few days stupidly and incorrectly claimed a proof of the irrationality of all after getting confused with a definition (sic) for which I express my deepest apologies for any confusion this may have caused, a new version of the preprint has withdrawn that claim.
The little that survives then is the formula which for , due to its product form, I thought might have some uses that the classical might not have.
Related expressions that I then obtained, namely
do not seem to be of any help towards a proof of irrationality of at least . A combination of those two expressions, perhaps with other expressions such as those of Vasilyev, might allow to improve matters, but I was not able to find how.