A few days ago I made a suggestion for an ordinary generating function (o.g.f.) for the Möbius function. Perhaps a silly suggestion. Might not even be possible. Anyways you can find it here: http://list.seqfan.eu/pipermail/seqfan/2010-November/006354.html
The o.g.f. I suggested was: a*sin(b*x)-c*tan(pi/2*x)+d*(cos(e*x)-1)+f*(1/cos(pi/2*x)-1).
Here b and e should perhaps be pi times some number. I tried b=e=pi and b=e=pi/2 but the fit from the the regression got worse. Yes I used regression to try to find the generating function for the power series. After a email response to my comment on the seqfan forum I am now more aware than before that the idea of an o.g.f. is to be precise. And I know my suggestion is incorrect.
Still I can’t completely give up thinking about whether it is possible to express the o.g.f for the Möbius function with trigonometric expressions.
Mats Granvik mats.granvik(AT)abo.fi