Difference between revisions of "Series for log(z) for absolute value of (z-1) less than 1"
From specialfunctionswiki
Line 6: | Line 6: | ||
==References== | ==References== | ||
− | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Series for log(z) for Re(z) greater than 1/2|next=}}: 4.1.26 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Series for log(z) for Re(z) greater than 1/2|next=Series for log(z) for Re(z) greater than 0}}: 4.1.26 |
Revision as of 07:43, 4 June 2016
Theorem
The following formula holds for $|z-1| \leq 1$ and $z \neq 0$: $$\log(z) = -\displaystyle\sum_{k=1}^{\infty} \dfrac{(-1)^k(z-1)^k}{k},$$ where $\log(z)$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.26