exp

---
description: Guidelines for exp
globs: **/*
---


 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).


 Internals

Mathematically, the exp function is defined for all real
valued arguments x as
 \[ \exp x \equiv e^{x}, \]
where
 \[ e = \sum_{0}^{\infty} \frac{1}{k!} \]
and is approximately 2.718281828459045 (returned by the
function e). For complex values z, the famous Euler formula
is used to calculate the exponential
 \[ e^{z} = e^{|z|} \left[ \cos \Re z + i \sin \Re z \right]
\]


 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))

 expplot1.png
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))

 expplot2.png

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* Mathematical_Functions
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