Difference between revisions of "Relationship between dilogarithm and log(1-z)/z"

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__NOTOC__
 
==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:
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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)
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* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Dilogarithm|next=Li2(z)=zPhi(z,2,1)}}: $\S 1.11.1 (22)$
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* {{BookReference|Dilogarithms and Associated Functions|1958|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$
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*{{BookReference|Polylogarithms and Associated Functions|1981|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Taylor series of log(1-z)|next=findme}}: $(1.3)$
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* {{BookReference|Structural Properties of Polylogarithms|1991|Leonard Lewin|prev=Dilogarithm|next=findme}}: $(1.2)$
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 23:23, 3 March 2018

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