# PolyLog Function

PolyLog Function

The polylogarithm function (or Jonquière's function) (z) of index and argument is a special function, defined in the complex plane for and by analytic continuation otherwise. It can be plotted for complex values ; for example, along the celebrated critical line for Riemann's zeta function [1]. The polylogarithm function appears in the Fermi–Dirac and Bose–Einstein distributions and also in quantum electrodynamics calculations for Feynman diagrams. The 2D plot shows the function , and the 3D plot shows .

Li

s

s

z

|z|<1

s=a+bi

s=1/2+bi

x⟶f((x+i))

Li

a+bi

b

0

(x,y)⟶f((x+yi))

Li

a+bi