Recursion, in the simplest terms, is a type of looping technique. It exploits the basic working of functions in R. Recursion is when the function calls itself. This forms a loop, where every time the function is called, it calls itself again and again and this technique is known as recursionhttps://www.geeksforgeeks.org/introduction-to-r-programming-language/. Since the loops increase the memory we use the recursion. The recursive function uses the concept of recursion to perform iterative tasks they call themselves, again and again, which acts as a loop. These kinds of functions need a stopping condition so that they can stop looping continuously.

Recursive functions call themselves. They break down the problem into smaller components. The function() calls itself within the original function() on each of the smaller components. After this, the results will be put together to solve the original problem.

Example: Factorial using Recursion in R

In R programming, a recursive function is a function that calls itself repeatedly until a certain condition is met. Recursive functions are useful when a problem can be broken down into smaller, similar subproblems. By using a recursive function, we can avoid duplicating code and make the code more concise and readable.

A basic example of a recursive function in R is the factorial function. The factorial of a positive integer n is the product of all positive integers from 1 to n. We can write a recursive function to calculate the factorial of a number as follows: 

factorial <- function(n) {
  if (n == 1) {
    return(1)
  } else {
    return(n * factorial(n - 1))
  }
}

In this function, the base case is when n equals 1, in which case the function returns 1. Otherwise, the function multiplies n by the factorial of n-1. The function continues to call itself with decreasing values of n until the base case is reached.

It's important to note that recursive functions can be memory-intensive and may cause a stack overflow if the number of function calls becomes too large. Therefore, it's important to choose an appropriate base case and ensure that the recursive function terminates within a reasonable number of iterations.