> Given that any recursive function can be written using a while loop with O(1) memory bounds I think that's only true if the function makes only one recursive

> Given that any recursive function can be written using a while loop with O(1) memory bounds I think that's only true if the function makes only one recursive call, like computing the Fibonacci numbers. If the function calls itself recursively twice, it may end up using a lot of memory, e.g. the Ackermann function.