gives the polylogarithm function .
gives the Nielsen generalized polylogarithm function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- PolyLog[n,z] 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.
Examplesopen allclose all
Basic Examples (6)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (5)
Function Properties (4)
Series Expansions (2)
Find the Taylor expansion using Series:
Function Identities and Simplifications (2)
PolyLog is defined through the identity:
Generalizations & Extensions (7)
Ordinary Polylogarithm Function (5)
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:
Nielsen Generalized Polylogarithm Function (2)
Plot of the absolute value of the dilogarithm function in the complex plane:
Calculate integrals over Fermi–Dirac distributions:
Plot the volume as a function of the vertex :
Mahler measure of the trivariate polynomial as a function of :
Plot the Mahler measure: