Recursive functions are defined by a function calling itself, which is useful for solving mathematical problems like calculating factorials and generating Fibonacci series. Advantages of recursion include maintaining function-related information and simplifying certain evaluations, while disadvantages involve slower performance and potential stack overflow issues. The document includes examples demonstrating recursion for calculating factorials and Fibonacci numbers in C programming.

1. Recursion Function
• A function is called ‘recursive’ if a statement
within the body of a function calls the same
function.
• In other word when a function call itself then
that function is called Recursive function.
• Recursive function are very useful to solve many
mathematical problems like to calculate
factorial of a number, generating Fibonacci
series, etc.

2. Advantage and Disadvantage
• Advantage of Recursion
– Function calling related information will be maintained
by recursion.
– Stack evaluation will be take place by using recursion.
– In fix prefix, post-fix notation will be evaluated by using
recursion.
• Disadvantage of Recursion
– It is a very slow process due to stack overlapping.
– Recursive programs can create stack overflow.
– Recursive functions can create as loops.

3. Example Factorial of a given Number
#include<stdio.h>
#include<conio.h>
int fact(int);
void main()
{
Int f,num;
clrscr();
printf("Enter any number: ");
scanf("%d",&num);
f=fact(num);
printf("Factorial: %d",f);
getch();
}
int fact(int n)
{
if(n<0)
printf("Error! Factorial of a negative
number doesn't exist.");
if(n==0)
return(1);
else
{
return(n*fact(n-1));
}
}
Output
Enter any number: 5
Factorial: 120

5. Example Fibonacci using Recursive
#include <stdio.h>
#include<conio.h>
int fibonacci(int i);
void main()
{
int i;
clrscr();
for (i = 0; i < 10; i++)
{
printf("%dtn", fibonacci(i));
}
getch();
}
int fibonacci(int i)
{
if(i == 0)
{ return 0; }
if(i == 1)
{ return 1; }
return fibonacci(i-1) +
fibonacci(i-2);
}
Output:
0 1 1 2 3 5 8 13 21 34