Formula:DLMF:25.12:E2

<< Formula:DLMF:25.12:E1

formula in Polylogarithms

Formula:DLMF:25.12:E3 >>

${\displaystyle{\displaystyle{\displaystyle\Dilogarithm@{z}=-\int_{0}^{z}t^{-1}\ln\left(1-t\right)\mathrm{d}t}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle z\in\Complex\setminus(1,\infty)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{Li}_{2}}}}$ : dilogarithm : http://dlmf.nist.gov/25.12#E1
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
${\displaystyle{\displaystyle{\displaystyle\mathrm{d}^{n}x}}}$ : differential : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\in}}}$ : element of : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r9
${\displaystyle{\displaystyle{\displaystyle\mathbb{C}}}}$ : set of complex numbers : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r1
${\displaystyle{\displaystyle{\displaystyle\setminus}}}$ : set subtraction : http://dlmf.nist.gov/front/introduction#Sx4.p2.t1.r19

Bibliography

Equation (2), Section 25.12 of DLMF.

URL links

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<< Formula:DLMF:25.12:E1

formula in Polylogarithms

Formula:DLMF:25.12:E3 >>