Jonquière's function

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z) congruent sum_(k = 1)^∞ z^k/k^n defined in the complex plane over the open unit disk. Its definition on the whole complex plane then follows uniquely via analytic continuation. Note that the similar notation Li(z) is used for the logarithmic integral.

dilogarithm | Eulerian number | Legendre's chi-function | logarithmic integral | multidimensional polylogarithm | Nielsen generalized polylogarithm | Nielsen-Ramanujan constants | trilogarithm