Difference between revisions of "Series for log(z) for Re(z) greater than 0"
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(Created page with "==Theorem== The following formula holds for $\mathrm{Re}(z) \geq 0, z \neq 0$: $$\log(z) = 2 \displaystyle\sum_{k=1}^{\infty} \left( \dfrac{z-1}{z+1} \right)^k \dfrac{1}{k},$$...") |
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Revision as of 07:47, 4 June 2016
Theorem
The following formula holds for $\mathrm{Re}(z) \geq 0, z \neq 0$: $$\log(z) = 2 \displaystyle\sum_{k=1}^{\infty} \left( \dfrac{z-1}{z+1} \right)^k \dfrac{1}{k},$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.27
