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) for Re(z) greater than 1/2}}: 4.1.24
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between logarithm and logarithm base 10|next=Series for 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