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PolyLog Function

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a
0.5
b
25.
b
0
0.86
f
Re
Im
Abs
Arg
view
2D
density
3D
The polylogarithm function (or Jonquière's function)
Li
s
(z)
of index
s
and argument
z
is a special function, defined in the complex plane for
|z|<1
and by analytic continuation otherwise. It can be plotted for complex values
s=a+bi
; for example, along the celebrated critical line
s=1/2+bi
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
x⟶f(
Li
a+bi
(x+
b
0
i))
, and the 3D plot shows
(x,y)⟶f(
Li
a+bi
(x+yi))
.
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