Difference between revisions of "Relationship between dilogarithm and log(1-z)/z"
From specialfunctionswiki
| Line 6: | Line 6: | ||
==References== | ==References== | ||
| − | {{BookReference|Polylogarithms and Associated Functions| | + | {{BookReference|Polylogarithms and Associated Functions|1981|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 04:21, 30 June 2016
Theorem
The following formula holds: $$\mathrm{Li}_2(z)=-\displaystyle\int_0^z \dfrac{\log(1-z)}{z} \mathrm{d}z,$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\log$ denotes the logarithm.
Proof
References
1981: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): $(1.3)$
