Repeated Application of User Defined Operators

Questions
1

Hello,

I created an operator:

op[x_] =  (D[#, x] + 3 x #) &

I can apply this to a function f[x] and create a new function as follows:

f1[x_] = op[x] [f[x]]

My question is: how can I apply the operator multiple times to f[x] in a single statement? I’d like to do this a large number of times, so I don’t want to use a large number of brackets.

Thanks, Joe

2

Maybe Nest?

Nest[op[x], f[x], 3]

Is that what you mean by “apply the operator multiple times”?

3

Yes, just what I was looking for. Thanks!