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Re: sequence of functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120168] Re: sequence of functions
  • From: rych <rychphd at gmail.com>
  • Date: Mon, 11 Jul 2011 06:56:58 -0400 (EDT)
  • References: <201107080855.EAA28789@smc.vnet.net> <iv9eqf$dfb$1@smc.vnet.net>

Yes, indeed, wrapping it with Evaluate did it. Thanks, Heike.

Bobby, f[n_][x_] :=  f[n][x] = ... results in caching for not only
each n and each x.

Dana, how did you apply FindSequenceFunction to get the direct
formula?!

Thanks
Igor



On Jul 9, 11:42 pm, Heike Gramberg <heike.gramb... at gmail.com> wrote:
> What about
>
> f[0] = Function[x, x (1 - x)]
> f[n_] := f[n] =
>    Function[x, Evaluate[Simplify[f[n - 1][2 x] + f[n - 1][2 x - 1]]]]=
;
>
> Then
>
> f[2][x];
> ?f
>
> returns:
>
> Global`f
> f[0]=Function[x,x (1-x)]
> f[1]=Function[x$,-2 (1-2 x$)^2]
> f[2]=Function[x$,-20+64 x$-64 x$^2]
> f[n_]:=f[n]=Function[x,Evaluate[Simplify[f[n-1][2 x]+f[n-1][2 x-1]]]]
>
> Heike



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