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Finite exponential series
Function
context | $ m\in{\mathbb N} |
definition | $\exp_n: \mathbb C\to\mathbb C$ |
definition | $\exp_n(z):=\sum_{k=0}^n \dfrac{1}{k!} z^k $ |
$\frac{\mathrm d}{\mathrm d z}\mathrm{exp}_0(z) = 1 $
$\mathrm{exp}_{n}(z) = \mathrm{exp}_{n-1}(z) + \dfrac{1}{n!} z^n$
Theorems
$\frac{\mathrm d}{\mathrm d z}\mathrm{exp}_0(z) = 0 $
$\frac{\mathrm d}{\mathrm d z}\mathrm{exp}_n(z) = \mathrm{exp}_{n-1}(z) = \mathrm{exp}_n(z) - \dfrac{1}{n!} z^n$
References
Wikipedia: Exponential function, Matrix exponential, Exponential map