Exponential

The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula $$\exp(z) = e^z = \sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ where $e$ is the base of the natural logarithm.

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  Graph of $\exp$.

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  Domain coloring of $\exp$.

Properties

Derivative of the exponential function
Taylor series of the exponential function
Exponential in terms of hypergeometric 0F0
Euler E generating function
Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt
Exponential function is periodic with period 2pii
Euler's formula

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.1