Difference between revisions of "Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))"
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Revision as of 20:19, 7 June 2016
Theorem
The following formula holds for all $z \in \mathbb{C}$: $$\left| e^z - 1 \right| \leq e^{|z|}-1 \leq |z| e^{|z|},$$ where $e^z$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 4.2.39
