Difference between revisions of "Abs(log(1+z)) less than or equal to -log(1-abs(z))"
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Latest revision as of 19:59, 25 June 2017
Theorem
The following formula holds for $|z|<1$: $$\left| \log(1+z) \right| \leq - \log(1-|z|),$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.38$
