Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Exp can take complex number inputs:

Evaluate Exp efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix Exp function using MatrixFunction:

The value at zero:

Values of Exp at fixed points:

Values at infinity:

Simple exact values are generated automatically:

Some more complicated values can be expanded using ExpToTrig:

Local extrema of Exp along the imaginary axis:

Find a value of for which the using Solve:

Substitute in the result:

Visualize the result:

Plot the Exp function:

Plot the real and imaginary parts of Exp[I x]:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

Exp is defined for all real and complex values:

Exp achieves all positive values on the reals:

The range for complex values is the entire plane except for 0:

Exp is a periodic function with period :

Exp has the mirror property :

Exp is an analytic function of x:

Exp is non-decreasing:

Exp is injective:

Exp is not surjective:

Exp is non-negative:

Has no singularities or discontinuities:

Exp is convex:

TraditionalForm formatting:

First derivative:

Formula for the derivative:

Derivative of a nested exponential function:

Indefinite integral of Exp:

Definite integral of Exp:

Gaussian integral:

Gamma function definition:

More integrals:

Taylor expansion for Exp:

Plot the first three approximations for Exp around :

General term in the series expansion of Exp:

Series expansion of the exponential function at infinity:

The first-order Fourier series:

Exp can be applied to power series:

Compute the Fourier transforms using FourierTransform:

LaplaceTransform:

MellinTransform:

Primary definition:

Euler's formula:

Convert from exponential to hyperbolic functions:

Convert trigonometric and hyperbolic functions into exponentials:

Products are automatically combined:

Expand assuming real variables x and y:

Exp arises from the power function in a limit:

Series representation:

Representation in terms of Bessel functions:

Exp can be represented in terms of MeijerG:

Exp can be represented as a DifferentialRoot:

Exponential decay:

Damped harmonic oscillator:

Solution of a boundary‐layer problem using Exp:

Plot various solutions:

Calculate the dispersion relation for the telegrapher's equation using a plane wave ansatz:

Solve the Schrödinger equation for the exponential Liouville potential:

Transmission and reflection coefficient of the Schrödinger equation for a step potential:

Propagator for the free‐particle Schrödinger equation:

Calculate spreading of a Gaussian wave packet:

Visualize the spreading:

Normal distribution:

Calculate moments:

Define the CDF of the Gumbel distribution through nested exponential functions:

Plot the PDF:

Calculate the first moment symbolically:

Define a Fermi–Dirac, a Bose–Einstein and a Maxwell–Boltzmann distribution function:

Plot the distributions:

Calculate the moments of the binomial distribution from the exponential generating function:

Multivariate Gaussian integrals:

Plot Fourier transforms:

Take this multivariate function:

Find series solution up to order three for the following system of equations:

The result satisfies the equations:

Construct a fast growing function using Exp and compute its limit: