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