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MathGroup Archive 2006

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general form of a n-derivative

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71542] general form of a n-derivative
  • From: Wiso <giurrerotipiacerebbe at hotmailtipiacerebbe.itipiacerebbe>
  • Date: Wed, 22 Nov 2006 05:22:23 -0500 (EST)
  • Organization: TIN.IT (http://www.tin.it)

Hi, I have this function:

\!\(f[x_] := Exp[\(-1\)/\((1 - x\^2)\)]\)

and these:

\!\(f\_n_[x_] := D[f[x], {x, n}]\)

the n-derivative. I try to evaluate some of these:
\!\(Table[FullSimplify[f\_i[x]], {i, 0, 5}]\  // TableForm\)

now I want to infer the general form with Mathematica(I think somethink
like:

(-1)^(2 n) (Exp[1/(1-x^2)])^(2 n) P(x), where P(x) is a poly in x). Some
ideas?


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