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Re: keep special functions unexpanded
*To*: mathgroup at smc.vnet.net
*Subject*: [mg131433] Re: keep special functions unexpanded
*From*: Bob Hanlon <hanlonr357 at gmail.com>
*Date*: Sun, 21 Jul 2013 21:43:37 -0400 (EDT)
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Re: "This technique also has the advantage that often your private
functions can be much neater in algebraic expressions - for example you can
use =CE=B3 to represent Gamma."
You can just set your output format to TraditionalForm or manually invoke
TraditionalForm
{Gamma[Pi], ChebyshevT[i, x], LaguerreL[n, a, x]} // TraditionalForm
Bob Hanlon
On Sun, Jul 21, 2013 at 4:24 AM, David Bailey <dave at removedbailey.co.uk>wrote:
> On 20/07/2013 10:56, metrologuy wrote:
> > I am trying to create a list of ChebyshevT[n,x] polynomials of different
> orders to use as basis functions in a fitting routine. I want to keep the
> list in the form that explicitly shows the order number. For example, I
> want the list for order n=2 to look like this:
> > basislist={ChebyshevT[0,x],ChebyshevT[1,x],ChebyshevT[2,x]}.
> > If I use Table to generate the list, I get each function expanded into a
> polynomial in x:
> >
> > In[1]:= Table[ChebyshevT[i,x],{i,0,2}]
> >
> > Out[1]= {1,x,-1+2 x^2}
> >
> > How can I prevent the function from displaying the expanded form for
> each value of n? If I use the unexpanded form in the Fit[] function, it
> works just fine. But I lose the visual connection to the explicit order
> number in the input form of the function. Any suggestions how to keep the
> "n" visible?
> >
> The best way to do this, is to use your own private notation for the
> function in question:
>
> basislist = {ChebT[0, x], ChebT[1, x], ChebT[2, x]}
>
> Replace the notation when you need to evaluate it:
>
> basislist /. ChebT -> ChebyshevT
>
> {1, x, -1 + 2 x^2}
>
> If you work with a lot of functions that you don't want to expand
> immediately, you can keep the list of transformations in a variable to
> simplify your work:
>
> functionActivations={ ChebT -> ChebyshevT, ChebU -> ChebyshevU};
>
> basislist /.functionActivations
>
>
> {1, x, -1 + 2 x^2}
>
> This technique also has the advantage that often your private functions
> can be much neater in algebraic expressions - for example you can use
> \[Gamma] to represent Gamma.
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
>
>
>
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