# Program to Calculate e^x by Recursion

The value of Exponential function can be calculated using Taylor Series.

= 1 + x/1! + /2! + /3! + ......

To find its value using recursion, we will use static variables. For the power of x we will use p and for factorials we will use f as static variables.
The function shown below is used to increase the power of x.

p = p*x

The function below is used to find factorials.

f = f*n

The function below is used to calculate the summation of the series.

r+p/f

where r is the recursive call to the function.

Below is the implementation of the above idea.

## C++

 // C++ implementation of the approach #include    // Recursive Function with static // variables p and f double e(int x, int n) {     static double p = 1, f = 1;     double r;        // Termination condition     if (n == 0)         return 1;        // Recursive call     r = e(x, n - 1);        // Update the power of x     p = p * x;        // Factorial     f = f * n;        return (r + p / f); }    // Driver code int main() {     int x = 4, n = 15;     printf("%lf \n", e(x, n));        return 0; }

## Java

 // Java implementation of the approach import java.text.*;    class GFG {        // Recursive Function with static // variables p and f static double p = 1, f = 1; static double e(int x, int n) {     double r;        // Termination condition     if (n == 0)         return 1;        // Recursive call     r = e(x, n - 1);        // Update the power of x     p = p * x;        // Factorial     f = f * n;        return (r + p / f); }    // Driver code public static void main (String[] args)  {     int x = 4, n = 15;     DecimalFormat df = new DecimalFormat("0.######");     System.out.println(df.format(e(x, n)));    } }    // This code is contributed by mits

## Python3

 # Python implementation of the approach    # Recursive Function  # global variables p and f p = 1.0 f = 1.0    def e(x, n) :        global p, f            # Termination condition     if (n == 0) :         return 1            # Recursive call     r = e(x, n - 1)            # Update the power of x     p = p * x            # Factorial     f = f * n            return (r + p / f)    # Driver code    x = 4 n = 15 print(e(x, n))    # This contributed by ihritik

## C#

 // C# implementation of the approach using System;    class GFG {        // Recursive Function with static // variables p and f static double p = 1, f = 1; static double e(int x, int n) {     double r;        // Termination condition     if (n == 0)         return 1;        // Recursive call     r = e(x, n - 1);        // Update the power of x     p = p * x;        // Factorial     f = f * n;        return (r + p / f); }    // Driver code static void Main() {     int x = 4, n = 15;     Console.WriteLine(Math.Round(e(x, n),6));    } }    // This code is contributed by mits

Output:

54.597883

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Improved By : Mithun Kumar, ihritik