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Exp

Exp[z]
gives the exponential of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For certain special arguments, Exp automatically evaluates to exact values.
  • Exp can be evaluated to arbitrary numerical precision.
  • Exp automatically threads over lists.
  • Exp[z] is converted to E^z.
EXAMPLESCLOSE ALL
Scope   (5)
Simple exact values are generated automatically:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Millions of digits can be computed in seconds:
Expand assuming real variables:
Products are automatically combined:
Generalizations & Extensions   (5)
Exp can deal with real-valued intervals:
Infinite arguments give symbolic results:
Exp can be applied to power series:
Exp threads element-wise over matrices:
Exp threads element-wise over sparse arrays:
Applications   (12)
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:
Properties & Relations   (16)
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 z-values:
Compose with inverse trigonometric and hyperbolic functions:
Solve transcendental equations involving Exp:
Reduce an exponential equation:
Integrals:
Integral transforms:
Sums:
The coefficients of the series of nested exponential functions are multiples of Bell numbers:
Exp is a numeric function:
Possible Issues   (7)
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 element-wise to matrices; MatrixExp finds matrix exponentials:
In traditional form parentheses are needed around the argument:
Neat Examples   (5)
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 n:
Nested exponential functions over the complex plane:
Fractal from iterating Exp:
The almost nowhere differentiable Riemann-Weierstrass function:
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