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Re: Re: Re: Arctangent approximation

Aha! I mistakenly thought the formula was a garbled version of the 
Taylor polynomial around 0.  (In general, one often uses something 
better than a Taylor polynomial, e.g., a Pade' approximation. But I was 
unaware of Medina's polynomial.)

My apologies to the OP (Sidey).

On 2/19/2010 3:32 AM, Louis Talman wrote:
> 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
>    <>

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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