I've not been able to find a precise definition of "stack depth" anywhere and have a rather simple question.
When dealing with trees I'm used to the maximum depth (or height) of the tree being the longest simple path between the root node and a leaf. For instance, if we had a longest simple path of length $n$, there would be $n+1$ nodes involved. In this case the height of the tree (or maximum depth) is $n$.
My question is, for "stack depth" and recursion, do we count the initial call to our procedure and all subsequent calls placed on the stack? Or do we exclude the initial call when counting stack depth?