Difference between revisions of "Exponential"
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The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula | The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula | ||
$$\exp(z) = e^z = \sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ | $$\exp(z) = e^z = \sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ | ||
Revision as of 21:14, 6 June 2016
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.
Graph of $\exp$.
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
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.1
