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Re: Re: Arctangent approximation

On Feb 18, 2010, at 3:15 AM, Murray Eisenberg wrote:

> I'll buy the first four terms of the approximation but not the fifth.
> What you seem to have here are the first 10 terms -- the first 5  
> nonzero
> terms -- of the Taylor expansion of ArcTan[x] around 0.

In fact, the polynomial given by Medina is a better approximation to  
the arctangent function---at least, roughly, when 0.2 < |x| < 1---than  
the degree 9 Maclaurin polynomial.  See Medina's paper for an idea of  
what he was up to.

--Lou Talman
   Department of Mathematical and Computer Sciences
   Metropolitan State College of Denver


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