What's the $e^{th}$ partial recursive function?

Question

What's the $e^{th}$ partial recursive function?

It refers here to the $e^{th}$ partial recursive function. Since no reference is provided, the reasonable implication seems to be that there's a canonical ordered set of such functions.

Answer 1

It is trivial to computably enumerate the partial recursive functions. Any such enumeration will do, and there is clearly no canonical sequence. No reference is provided because it is an extremely basic concept in computability theory. Same if you see phrases like "$k$-th program" or "$k$-th Turing machine".