# What is the precise mathematical definition of n-iterated recusion?

Primitive recursion can be extended to double-recursion as in the following link:

http://www.andrew.cmu.edu/user/kk3n/recursionclass/1primrec.html

How can this be generalized to n-iterated recursion? I got the term "n-iterated recursion" from Hans Hyttel on Quora. The idea is that double-recursion extends primitive recursion in a manner similar to the way that (n+1)-iterated recursion extends n-iterated recursion. I am looking for a clear function based definition, similar to the definition of primitive recursion and double-recursion in the link above.