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.
- Exp can be used with Interval and CenteredInterval objects. »
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Basic Examples (6)
Numerical Evaluation (6)
Exp can take complex number inputs:
Evaluate Exp efficiently at high precision:
Exp threads elementwise over lists and matrices:
Specific Values (6)
Values of Exp at fixed points:
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:
Function Properties (12)
Exp is defined for all real and complex values:
Exp achieves all positive values on the reals:
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:
Exp is convex:
Series Expansions (5)
Integral Transforms (3)
Function Identities and Simplifications (6)
Solution of a boundary‐layer problem using Exp:
Calculate the moments of the binomial distribution from the exponential generating function:
Construct a fast growing function using Exp and compute its limit:
Properties & Relations (19)
Exp arises from the power function in a limit:
Solve transcendental equations involving Exp:
Exp is a numeric function:
The generating function for Exp:
The exponential generating function for Exp:
Possible Issues (7)
Literal matchings may fail because exponential functions evaluate to powers with base E:
Use Together to remove logarithms in exponents:
No power series exists at infinity, where Exp has an essential singularity:
In TraditionalForm input, parentheses are needed around the argument:
Neat Examples (5)
Closed-form expression for the partial sum of the power series of Exp:
Leading correction for the difference to Exp[z] for large :
Fractal from iterating Exp:
Wolfram Research (1988), Exp, Wolfram Language function, https://reference.wolfram.com/language/ref/Exp.html (updated 2021).
Wolfram Language. 1988. "Exp." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Exp.html.
Wolfram Language. (1988). Exp. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Exp.html