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Re: ChebyshevT command syntax and polynomial question using

• To: mathgroup at smc.vnet.net
• Subject: [mg88298] Re: ChebyshevT command syntax and polynomial question using
• From: ratullochjk2 at gmail.com
• Date: Thu, 1 May 2008 03:19:40 -0400 (EDT)
• References: <fv9af1$ms0$1@smc.vnet.net> <fv9ju0$54j$1@smc.vnet.net>

thanks but when I test for x =3 x= 7
21 - 10 x + x^2 I get zero for both answers
1/2 Cos[2 ArcCos[x]] + 43/2 - 10 x  also gives me zero for both

but when I do a TrigReduce

In[148] := 21 - 10 x + x^2 /. x -> Cos[y] // TrigReduce

I get

Out[149]:= 1/2 (43 - 20 Cos[x] + Cos[2 x])
x=3 gives me 31.88
x=7 gives me 14.0293

Am I doing something wrong or leaving a part out?
tia sal2

On Apr 30, 1:07 am, Szabolcs Horv=E1t <szhor... at gmail.com> wrote:
> ratulloch... at gmail.com wrote:
> > Greetings All
>
> > I execute the command and get the following output:
>
> > In[83] := FunctionExpand[1/2 Cos[2 ArcCos[x]] + 43/2 - 10 x] // Expand=

> > Out[83]:= 21 - 10 x + x^2
>
> > What would be the proper format to execute the polynomial using
> > ChebyshevT to do it in reverse order?
>
> > Example:
> > I would input
> > In[83] := FunctionExpand[ChebyshevT[n, x]]
> > and it gives me
> > Out[83]:= Cos[n ArcCos[x]]
>
> > How can I do a
> > In[83] := FunctionExpand[ChebyshevT[n, x]]
> > and it would give me
> > Out[83]:= 1/2 Cos[2 ArcCos[x]] + 43/2 - 10 x
>
> Use TrigReduce:
>
> 21 - 10 x + x^2 /. x -> Cos[y] // TrigReduce