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Re: How to apply a function to a function multiple times

• To: mathgroup at smc.vnet.net
• Subject: [mg73470] Re: [mg73457] How to apply a function to a function multiple times
• From: luhao <luhaorice at gmail.com>
• Date: Sun, 18 Feb 2007 06:14:34 -0500 (EST)
• References: <200702171002.FAA26271@smc.vnet.net>

Peng Yu wrote:
> Hi,
> 
> I have the following code.
> 
> iterater[hPrev_] := Integrate[Sqrt[1 + Derivative[1, 0][hPrev][x, t]^2], t]*v[x]
> h0[x_,t_]:=0
> h1[x_,t_]:=iterater[h0]
> h2[x_,t_]:=iterater[h1]
> h3[x_,t_]:=iterater[h2]
> 
> 
> I want to code another function,
> fun[h0_,v_,n_]
> where n is the times "iterator" has been applied.
> fun[h0,v,3] should give me h3[x_,t_] defined above.
> 
> fun[h0,v,4] should give me iterator[h3].
> 
> Can you show me how to do it?
> 
> Thank,
> Peng
> 
>

I believe Nest[] is what you want.

Hao

• References:
  • How to apply a function to a function multiple times
    • From: "Peng Yu" <pengyu.ut@gmail.com>