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gives the polylogarithm function .
gives the Nielsen generalized polylogarithm function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • .
  • .
  • PolyLog has a branch cut discontinuity in the complex plane running from 1 to .
  • For certain special arguments, PolyLog automatically evaluates to exact values.
  • PolyLog can be evaluated to arbitrary numerical precision.
  • PolyLog automatically threads over lists.
Click for copyable input
Click for copyable input
Click for copyable input
Simple exact values are generated automatically:
Evaluate with large order and argument:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex order and arguments:
PolyLog threads element-wise over lists:
TraditionalForm formatting:
Infinite arguments give symbolic results:
PolyLog can be applied to power series:
Evaluate derivatives exactly:
Series expansion at branch cuts:
Series expansion at infinity:
Give the result for an arbitrary symbolic direction:
Special cases:
Series expansion:
Plot of the absolute value of the dilogarithm function in the complex plane:
Calculate integrals over Fermi-Dirac distributions:
Volume of a hyperbolic dodecahedron with vertices 0, 1, , (subject to ):
Plot the volume as a function of the vertex :
Mahler measure of the trivariate polynomial as a function of :
Plot the Mahler measure:
Use FullSimplify to simplify polylogarithms:
Use FunctionExpand to expand polylogarithms:
Numerically find a root of a transcendental equation:
Generate from integrals and sums:
PolyLog appears in special cases of various mathematical functions:
Large orders can give results too large to be computed explicitly:
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