Re: keep special functions unexpanded

*To*: mathgroup at smc.vnet.net*Subject*: [mg131417] Re: keep special functions unexpanded*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Sun, 21 Jul 2013 04:24:17 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <ksdmsm$50s$1@smc.vnet.net>

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