Difference between revisions of "Relationship between dilogarithm and log(1-z)/z"
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(Created page with "==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 $\...") |
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==References== | ==References== | ||
| − | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev= | + | {{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) |
Revision as of 23:53, 3 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)
