scipy.special.spence¶

scipy.special.spence(z) = <ufunc 'spence'>

Spence’s function, also known as the dilogarithm. It is defined to be

$\int_0^z \frac{\log(t)}{1 - t}dt$

for complex $$z$$, where the contour of integration is taken to avoid the branch cut of the logarithm. Spence’s function is analytic everywhere except the negative real axis where it has a branch cut.

Note that there is a different convention which defines Spence’s function by the integral

$-\int_0^z \frac{\log(1 - t)}{t}dt;$

this is our spence(1 - z).

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