It’s more or less a consequence of http://en.wikipedia.org/wiki/Interesting_number_paradox applied to special functions. What are the opposites? General functions? There are generalized functions, like the Meijer-G function, but that seems kind of contrary to the point (they do have their applications, for example, Mathematica uses the Meijer-G function internally, but it’s not the sort of function which seems very user friendly).
I’m going to kind of rally against some of the attitude espoused in this question:
Most real numbers are transcendental. Yes, they probably satisfy scads of strange identities. Do those identities conform to toolbox-fetishist-expectations of how the real or complex numbers work? Some of them do. But after a point, those are uninteresting and trivial. Most of the time I care about identities between functions and I live on the rainbow world of the complex plane, so mere identities between infinite series or products kind of fade. And, you know, you don’t have any of the tools of alien mathematics in that toolbox of yours. There are functions and relations which are undreamt of in that Primate sandbox of yours, so stop saber-rattling that toolbox.