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MathGroup Archive 2005

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Composition of Expansions

  • To: mathgroup at
  • Subject: [mg54982] Composition of Expansions
  • From: "Scott Guthery" <sguthery at>
  • Date: Tue, 8 Mar 2005 05:04:52 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Bf[f_] := Sum[f[i/100]B[i,100,x],{i,0,100}]

gives the Bernstein expansion of f.

Df[f_] := 1-Bf[f]

is a function of interest.  I want to work with

Df[Df[Df[...[Df[g]]...]]] for some g[x_] := ...

i.e Bernstein expansions of Bernstein expansions.

As a simple example, suppose g[x_] := x^2 and try

Plot[Composition[Df, Df[g]], {x, 0, 1}]

Composition[Df, Df[g]] does not compute.

Thanks for any insight.

Cheers, Scott




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