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Re: ChebyshevT command syntax and polynomial question using mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg88287] Re: ChebyshevT command syntax and polynomial question using mathematica
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Wed, 30 Apr 2008 07:03:11 -0400 (EDT)
• Organization: University of Bergen
• References: <fv9af1$ms0$1@smc.vnet.net>

ratullochjk2 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