[Newbie] expansion of a function as a power series
Subject: [Newbie] expansion of a function as a power series
From: Barton Willis
Date: Wed, 25 Jul 2007 13:17:48 -0500
If you download the CVS version of series, you can do this:
(%i1) load("C:/maximacvs3/src/series.lisp")$
(%i2) powerseries(x/(1-x-x^2),x,0);
(%o2)
-x*sum((-(2*(sqrt(5)-1)^(-i1-1)*2^i1)/sqrt(5)-(2*(sqrt(5)+1)^(-i1-1)*(-2)^i1)/sqrt(5))*x^i1,i1,0,inf)
The coefficient of x^i1 is
(%i3) first(first(last(last(%))));
(%o3)
-(2*(sqrt(5)-1)^(-i1-1)*2^i1)/sqrt(5)-(2*(sqrt(5)+1)^(-i1-1)*(-2)^i1)/sqrt(5)
The first(first(last(last(...))) is ugly. For the CVS version of series,
go to
http://maxima.cvs.sourceforge.net/maxima/maxima/src/
download the file series.lisp; put the file anywhere. You might
need to load it using a full path name (as I did in (%i1)).
Barton
maxima-bounces at math.utexas.edu wrote on 07/25/2007 11:16:54 AM:
> Can anyone tell me how to "harvest" the coefficient of x^n in the
> expansion of the function x/(1-x-x?^2) as a ower series around the
origin?
>
> regards,
> hugo
>
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