Difference between revisions of "Relationship between dilogarithm and log(1-z)/z"
From specialfunctionswiki
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
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==References== | ==References== | ||
* {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$ | * {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$ | ||
| − | {{BookReference|Polylogarithms and Associated Functions|1981|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$ | + | *{{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 04:32, 7 July 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
- 1958: Leonard Lewin: Dilogarithms and Associated Functions ... (previous) ... (next): $(1.3)$
- 1981: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): $(1.3)$
