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MathGroup Archive 2007

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Re: Paul Abbott Chebyshev Article

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79751] Re: Paul Abbott Chebyshev Article
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Fri, 3 Aug 2007 06:32:21 -0400 (EDT)

One more:  Here it is in InputForm:

In[22]:=
n = 4; xs = N[Cos[(Range[0, 2*n]*Pi)/(2*n)], 20]

cs = Thread[Subscript[c, Range[0, n]]]

lhs = cs . Table[ChebyshevT[2*i, xs], {i, 0, n}]; 

rhs = 1 + (1/Pi)*cs . Table[NIntegrate[
        Evaluate[ChebyshevT[2*i, t]/((xs - t)^2 + 
           1)], {t, -1, 1}, WorkingPrecision -> 
         20], {i, 0, n}]; 

sol = Solve[lhs == rhs, cs]; 

f[x_] = Sum[Subscript[c, i]*ChebyshevT[2*i, x], 
     {i, 0, n}] /. First[sol] 

Plot[f[x], {x, -1, 1}]

Now cut/paste this into a notebook and switch the Cell to Traditional form and the ChebyshevT will get converted to T_n.


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