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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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936|next=}}: 4.2.38 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936|next=abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))}}: 4.2.38 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
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) ... (next): 4.2.38
