Euler's dilogarithm

The dilogarithm Li_2(z) is a special case of the polylogarithm Li_n(z) for n = 2. Note that the notation Li_2(x) is unfortunately similar to that for the logarithmic integral Li(x). There are also two different commonly encountered normalizations for the Li_2(z) function, both denoted L(z), and one of which is known as the Rogers L-function. The dilogarithm is implemented in the Wolfram Language as PolyLog[2, z]. The dilogarithm can be defined by the sum Li_2(z) = sum_(k = 1)^∞ z^k/k^2 or the integral Li_2(z) congruent integral_z^0 (ln(1 - t) d t)/t.

Abel's duplication formula | Abel's functional equation | Clausen function | inverse tangent integral | L-algebraic number | Legendre's chi-function | logarithm | polylogarithm | Rogers L-function | Spence's function | Spence's integral | trilogarithm | Watson's identities