Difference between revisions of "Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1"
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(Created page with "==Theorem== The following formula holds for $|z| \geq 1, z \neq \pm 1$: $$\log \left( \dfrac{z+1}{z-1} \right) = 2 \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(2k+1)z^{2k+1}},$...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Series for log(z) for Re(z) greater than 0|next=Series for log(z+a) for positive a and Re(z) greater than -a}}: 4.1.28 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Series for log(z) for Re(z) greater than 0|next=Series for log(z+a) for positive a and Re(z) greater than -a}}: $4.1.28$ |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 17:28, 27 June 2016
Theorem
The following formula holds for $|z| \geq 1, z \neq \pm 1$: $$\log \left( \dfrac{z+1}{z-1} \right) = 2 \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(2k+1)z^{2k+1}},$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.28$
