Difference between revisions of "Relationship between dilogarithm and log(1-z)/z"
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==References== | ==References== | ||
{{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Taylor series of log(1-z)|next=Derivative of Li_2(-1/x)}}: (1.3) | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Taylor series of log(1-z)|next=Derivative of Li_2(-1/x)}}: (1.3) | ||
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 20:23, 27 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
1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): (1.3)
