## EXP Exponential Function

Section: Mathematical Functions

### Usage

Computes the `exp` function for its argument. The general syntax for its use is

       y = exp(x)

where `x` is an `n`-dimensional array of numerical type. Integer types are promoted to the `double` type prior to calculation of the `exp` function. Output `y` is of the same size and type as the input `x`, (unless `x` is an integer, in which case `y` is a `double` type).

### Function Internals

Mathematically, the `exp` function is defined for all real valued arguments `x` as

where

and is approximately `2.718281828459045` (returned by the function `e`). For complex values `z`, the famous Euler formula is used to calculate the exponential

### Example

The following piece of code plots the real-valued `exp` function over the interval `[-1,1]`:

    --> x = linspace(-1,1);
    --> plot(x,exp(x))
    -->
    quit

In the second example, we plot the unit circle in the complex plane `e^{i 2 pi x}` for `x in [-1,1]`.

    --> x = linspace(-1,1);
    --> plot(exp(-i*x*2*pi))
    -->
    quit