How to apply a function to a function multiple times

*To*: mathgroup at smc.vnet.net*Subject*: [mg73457] How to apply a function to a function multiple times*From*: "Peng Yu" <pengyu.ut at gmail.com>*Date*: Sat, 17 Feb 2007 05:02:03 -0500 (EST)

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

**Follow-Ups**:**Re: How to apply a function to a function multiple times***From:*luhao <luhaorice@gmail.com>