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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

Context

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