Difference between revisions of "Taylor series of log(1+z)"
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between logarithm and logarithm base 10|next=Taylor series of log(z)}}: 4.1.24 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between logarithm and logarithm base 10|next=Taylor series of log(z) for Re(z) greater than 1/2}}: 4.1.24 |
Revision as of 07:33, 4 June 2016
Theorem
The following formula holds for $|z| \leq 1$ and $z \neq -1$: $$\log(1+z)=-\displaystyle\sum_{k=1}^{\infty} \dfrac{(-1)^kz^k}{k},$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.24
