|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:application
|
gptkb:quantum_field_theory
gptkb:Feynman_integrals
knot theory
|
|
gptkbp:definedIn
|
series expansion
|
|
gptkbp:domain
|
complex numbers
|
|
gptkbp:field
|
gptkb:mathematics
complex analysis
mathematical physics
number theory
|
|
gptkbp:generalizes
|
logarithm
dilogarithm
trilogarithm
|
|
gptkbp:hasSpecialCase
|
polylogarithm order 1 is logarithm
polylogarithm order 2 is dilogarithm
polylogarithm order 3 is trilogarithm
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
polylogarithms
|
|
gptkbp:introduced
|
gptkb:Leonhard_Euler
|
|
gptkbp:notation
|
Li_s(z)
|
|
gptkbp:parameter
|
complex parameter s
|
|
gptkbp:range
|
complex numbers
|
|
gptkbp:relatedTo
|
gptkb:lion
gptkb:Riemann_zeta_function
gptkb:Hurwitz_zeta_function
gptkb:Clausen_function
multiple zeta values
|
|
gptkbp:seriesDefinition
|
Li_s(z) = sum_{k=1}^∞ z^k / k^s
|
|
gptkbp:usedIn
|
gptkb:theoretical_physics
mathematical research
|
|
gptkbp:variant
|
complex variable z
|
|
gptkbp:bfsParent
|
gptkb:motivic_polylogarithms
|
|
gptkbp:bfsLayer
|
7
|