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MathGroup Archive 2007

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Re: Paul Abbott Chebyshev Article

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79748] Re: Paul Abbott Chebyshev Article
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Fri, 3 Aug 2007 06:30:47 -0400 (EDT)

Now I understand . . . he's using Traditional Form to specify ChebyshevT and that's T_n.  Apparently he's doing so via this command:

Cell[BoxData[
    \(TraditionalForm\`Attributes[ChebyshevT]\)], "Input"]

(but I'm not used to such notation).  Also, he's solving  Love's Equation:

f[x]=1+1/pi Integrate[f[t]/((x-t)^2+1)dt,{t,-1,1}]

I'd take apart the algorithm:  Split-out all the commands, and execute them one by one WITHOUT the semicolons to see what's happening.


> n=4; xs = N[Cos[Range[0, 2 n] Pi/(2 n)], 20];
> cs = Thread[Subscript[c, Range[0, n]]];
> lhs = cs.Table[Subscript[T, 2 i] (xs), {i, 0, n}];
> rhs = 1 + 1/Pi
> cs.Table[NIntegrate[Evaluate[Subscript[T, 2 i]
> (t)/((xs - 
> t)^2 + 1)], {t, -1, 1}, WorkingPrecision ->20], {i,
> 0, n}];
> 
> the last line of code keeps giving me the error that
> "NIntegrate::inumr: 
> The integrand (t
> Subscript[T,0])/(1+(1.0000000000000000000-t)^2) has 
> evaluated to non-numerical values for all sampling
> points in the region 
> with boundaries {{-1,0}}. >>
> 
> I'm not quite sure why this is the case?
>


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