What defines a recursive function?

A recursive function is defined as one that calls itself in order to solve a problem. This self-referential characteristic allows recursive functions to break down complex problems into smaller, more manageable subproblems. Each call to the function works towards reaching a base case, which stops the recursion and begins returning results back up the call stack.

For instance, in calculating the factorial of a number, a recursive function will call itself with a decremented argument until it reaches the base case (often when the input is 1 or 0). This technique is powerful for solving problems that can be defined in terms of similar subproblems, such as traversing tree structures, generating permutations, or implementing algorithms like quicksort and mergesort.

The concept of recursion differs from functions that merely call other functions but do not call themselves, or from functions that might be executed only once without any recursion or repetition in their logic. Thus, the defining feature of a recursive function is its ability to invoke itself.