Re: Composition of Expansions

*To*: mathgroup at smc.vnet.net*Subject*: [mg55014] Re: Composition of Expansions*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>*Date*: Wed, 9 Mar 2005 06:34:40 -0500 (EST)*References*: <d0jv47$n75$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Scott Guthery wrote: > 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 > > > > > > <https://mail2.mobile-mind.com/exchange/sguthery/Drafts/RE:%20%20New%20in%205.1.1_x003F_.EML/#> > Hi, Composition is an operation that takes two functions and returns a function: h = Composition[f, g] Composition[f, g] h[x] f[g[x]] However, for repeated application of the same function, it is easier to use Nest: Nest[f, x, 6] f[f[f[f[f[f[x]]]]]] Regards, David Bailey dbaileyconsultancy.co.uk