Evaluate numerically:

Evaluate numerically to any precision:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion at the origin:

Exponential functions can be entered as ee x:

Exponential decay:

Damped harmonic oscillator:

Normal distribution:

Calculate moments:

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

Plot the PDF:

Calculate the first moment symbolically:

Solution of a boundary‐layer problem using Exp:

Plot various solutions:

Multivariate Gaussian integrals:

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

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

Plot the distributions:

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:

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

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:

Convert from Exp to Power:

Convert from exponential to trigonometric and hyperbolic functions:

Convert trigonometric and hyperbolic functions into exponentials:

Calculate special values as radicals:

Extract numerators and denominators:

Reciprocals of the exponential function evaluate to exponential functions:

Exp arises from the power function in a limit:

Compose with inverse functions:

PowerExpand disregards multivaluedness of Log:

Obtain a form correct for all complex ‐values:

Compose with inverse trigonometric and hyperbolic functions:

Solve transcendental equations involving Exp:

Reduce an exponential equation:

Integrals:

Integral transform:

Sums:

The coefficients of the series of nested exponential functions are multiples of Bell numbers:

Exp is a numeric function:

The generating function for Exp:

FindSequenceFunction can recognize the Exp sequence:

The exponential generating function for Exp:

Exponentials can be very large:

And can become too large for computer representation of a number:

Literal matchings may fail because exponential functions evaluate to powers with base E:

Use Unevaluated or Hold to avoid evaluation:

Logarithms in exponents are not always automatically resolved:

Use Together to remove logarithms in exponents:

Machine-precision input is insufficient to give a correct answer:

With exact input, the answer is correct:

No power series exists at infinity, where Exp has an essential singularity:

Exp is applied elementwise to matrices; MatrixExp finds matrix exponentials:

In TraditionalForm input, parentheses are needed around the argument:

Find correction terms to a classic limit:

Closed-form expression for the partial sum of the power series of Exp:

Leading correction for the difference to Exp[z] for large :

Nested exponential functions over the complex plane:

Fractal from iterating Exp:

The almost nowhere differentiable Riemann–Weierstrass function: