Relationship between dilogarithm and log(1-z)/z

From specialfunctionswiki
Revision as of 23:23, 3 March 2018 by Tom (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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