About my generating function attempt

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

Advertisements
This entry was posted in Uncategorized. Bookmark the permalink.