Revision as of 21:00, 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.

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

References

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