## 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))

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))