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

From specialfunctionswiki
Jump to: navigation, search
Line 6: Line 6:
  
 
==References==
 
==References==
 +
* {{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 04:27, 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): $(1.3)$