Difference between revisions of "Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1"
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(Created page with "==Theorem== The following formula holds for $0<|z|<1$: $$\dfrac{|z|}{4} < |e^z-1| < \dfrac{7|z|}{4},$$ where $e^z$ denotes the exponential. ==Proof== ==References== * {{...") |
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Revision as of 20:17, 7 June 2016
Theorem
The following formula holds for $0<|z|<1$: $$\dfrac{|z|}{4} < |e^z-1| < \dfrac{7|z|}{4},$$ where $e^z$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 4.2.38
