Difference between revisions of "Taylor series of log(1-z)"

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=References=
 
=References=
{{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: (1.2)
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* {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: $(1.2)$
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*{{BookReference|Polylogarithms and Associated Functions|1981|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: $(1.2)$
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 04:28, 7 July 2016

Theorem

The following formula holds: $$\log(1-z)=-\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k},$$ where $\log$ denotes the logarithm.

Proof

References