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How to apply a function to a function multiple times


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


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