
Re: keep special functions unexpanded
Posted:
Jul 21, 2013 4:16 AM


You could try something like this:
MakeBoxes[HoldForm[ChebyshevT[n_, x_]], form : StandardForm  TraditionalForm] := InterpretationBox[#1, #2] & @@ {RowBox[{SubscriptBox["T", MakeBoxes[n, form]], "[", MakeBoxes[x, form], "]"}], ChebyshevT[n, x]}
Then with regular Mathematica:
fitFunctions = Table[HoldForm[ChebyshevT[ii, x]] /. ii > i, {i, 0, 2}] % // ReleaseHold
{Subscript[T, 0][x], Subscript[T, 1][x], Subscript[T, 2][x]} {1, x, 1 + 2 x^2}
Or with Presentations you could use:
fitFunctions = Table[ChebyshevT[i, x], {i, 0, 2}] // HoldOp[ChebyshevT]
with the same output.
Then with Fit you might use:
data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}}; Fit[data, fitFunctions // ReleaseHold, x] Cases[%, Alternatives @@ Flatten[{a_Real, a_ Rest@ReleaseHold[fitFunctions]}] > a].fitFunctions
0.773869  0.266332 x + 0.0954774 (1 + 2 x^2) 0.773869 Subscript[T, 0][x]  0.266332 Subscript[T, 1][x] + 0.0954774 Subscript[T, 2][x]
David Park djmpark@comcast.net http://home.comcast.net/~djmpark/index.html
From: metrologuy [mailto:takacs@bnl.gov]
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?

