Re: Re: Re: Arctangent approximation
- To: mathgroup at smc.vnet.net
- Subject: [mg107649] Re: [mg107593] Re: [mg107578] Re: [mg107560] Arctangent approximation
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sun, 21 Feb 2010 04:25:39 -0500 (EST)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <201002171202.HAA21864@smc.vnet.net> <201002181015.FAA28477@smc.vnet.net> <201002190832.DAA00761@smc.vnet.net>
- Reply-to: murray at math.umass.edu
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 > > <http://rowdy.mscd.edu/%7Etalmanl> > > > > -- Murray Eisenberg murray at math.umass.edu 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
- References:
- Arctangent approximation
- From: sidey <sidey.p.timmins@census.gov>
- Re: Arctangent approximation
- From: Murray Eisenberg <murray@math.umass.edu>
- Re: Re: Arctangent approximation
- From: Louis Talman <talmanl@gmail.com>
- Arctangent approximation