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.