Difference between revisions of "Taylor series of log(1-z)"
From specialfunctionswiki
| Line 8: | Line 8: | ||
=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) | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[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)
