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)
 
{{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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[[Category:Theorem]]
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[[Category:Unproven]]

Revision as of 20:25, 27 June 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

1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): (1.2)