(Why) is there no recursion pointer in C++?

Question

In C++ every object has a pointer called "this" which points to the object itself.
1.) Is there also a pointer pointing to the function in which it is called?
2.) If not, why?
Advantages: If you change the function name you wouldn't have to change every recursive function call inside that function. That would also help you to avoid errors.
Disadvantage: could be less readable?
3.) Do other languages have this feature?
Example (I called the pointer to the function it ist called in "recursion"):
// you could e.g. write this:
void func(int i) { recursion(i); }
// instead of this:
void func(int i) { func(i); }

Answer 1

I actually like the idea. It's not useful for what you described, because you can just use the name of the function, but some functions don't have names:
[](int n) -> int {
// this is an anonymous function.
// How can I possibly recurse here?
}
Javascript actually had a "recursion pointer", called `arguments.callee`. It is deprecated... but because of obscure javascript problems and not because it's a bad idea per se.
I'm all for it even though the use cases are pretty limited.
And as far as programming theory goes, you can implement a "recursion operator" that will pass the function you apply it to as it's first parameter, in pretty much any programming language. It's called the Y combinator and it is my profile status, check it out :)
You'd use it like this (pseudocode, assuming `Y` is correctly implemented):
Y(fn (recurse, n) {
if n == 0: return;
recurse(n-1);
})(10);

Answer 2

Yes, you are right. It's much more convenient to write
auto func = [](int i){ recursion(i); };
instead of
std::function<void(int)> func = [&func](int i){ func(i); };

Answer 3

thats a good solution but you still have the problem that you have to store the function pointer in a variable. I think Y combinators are a better technique to solve the problem