# PHP - Recursive Function

A function which can call itself is known as recursive function. A recursive function generally ends with one or more boundary conditions which defines exit conditions from the function, otherwise it will go into an infinite loop.

### Example: Factorial of a number

The factorial of a positive integer is the multiplication of all positive integer less than or equal to that number.

factorial of number n = n! = n(n-1)(n-2)...1

In the example below, a recursive function called factorial() is used to calculate factorial of a number.

```<?php
function factorial(\$x) {
if (\$x == 0 || \$x == 1)
return 1;
else
return \$x*factorial(\$x-1);
}

echo "3! =  ".factorial(3)."\n";
echo "5! =  ".factorial(5)."\n";
echo "10! =  ".factorial(10)."\n";
?>
```

The output of the above code will be:

```3! =  6
5! =  120
10! =  3628800
```

### Example: Fibonacci Sequence

Fibonacci terms are generally represented as Fn. A Fibonacci term is the sum of two previous terms and starts with 0 and 1. Mathematically, it can be represented as:

Fn = Fn-1 + Fn-2

With boundary conditions: F0 = 0 and F1 = 1

The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

In the example below, a recursive function called fib() is created to find out the nth term of Fibonacci sequence.

```<?php
function fib(\$n) {
if (\$n == 0)
{return 0;}
elseif (\$n == 1)
{return 1;}
else
{return fib(\$n-1) + fib(\$n-2);}
}

echo "Fibonacci 5th term: ".fib(5)."\n";
echo "Fibonacci 6th term: ".fib(6)."\n";
echo "Fibonacci 7th term: ".fib(7)."\n";
?>
```

The above code will give the following output:

```Fibonacci 5th term: 5
Fibonacci 6th term: 8
Fibonacci 7th term: 13
```

❮ PHP - Functions

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