Difference between revisions of "Taylor series of log(1-z)"
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=References= | =References= | ||
* {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: $(1.2)$ | * {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: $(1.2)$ | ||
| − | *{{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) | + | *{{BookReference|Polylogarithms and Associated Functions|1981|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Dilogarithm|next=Relationship between dilogarithm and log(1-z)/z}}: $(1.2)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[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
- 1958: Leonard Lewin: Dilogarithms and Associated Functions ... (previous) ... (next): $(1.2)$
- 1981: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): $(1.2)$
