The basic definition would be something like use of a function in that function's own code. It's pretty easy to find examples that aren't tail-recursive specifically, like mergesort, and examples within those that would overflow a hardware stack, like in OP. And that's without looking at (mildly) exotic examples like the Ackermann function.

Basically, the "Please leave recursion to math and keep it out of (in particular C) software" in OP means don't define functions using those functions. It's pretty and it can work, but not reliably.