Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Special function
|
| gptkbp:alsoKnownAs |
Spence's function
|
| gptkbp:appearsIn |
gptkb:Algebraic_K-theory
gptkb:quantum_field_theory gptkb:Number_theory |
| gptkbp:branch |
z=1
z=∞ |
| gptkbp:definedIn |
Li₂(z) = -∫₀^z (ln(1-t)/t) dt
|
| gptkbp:differential |
d/dz Li₂(z) = -ln(1-z)/z
|
| gptkbp:domain |
gptkb:Complex_numbers
|
| gptkbp:functionalEquation |
Li₂(z) + Li₂(1-z) = π²/6 - ln(z)ln(1-z)
|
| gptkbp:generalizes |
gptkb:Polylogarithm
gptkb:Trilogarithm Logarithm |
| gptkbp:hasSpecialCase |
Li₂(-1) = -π²/12
Li₂(0) = 0 Li₂(1) = π²/6 |
| https://www.w3.org/2000/01/rdf-schema#label |
Dilogarithm
|
| gptkbp:namedAfter |
gptkb:William_Spence
|
| gptkbp:relatedTo |
gptkb:Riemann_zeta_function
gptkb:Polylogarithm Logarithm |
| gptkbp:seriesExpansion |
Li₂(z) = Σ_{k=1}^∞ z^k / k²
|
| gptkbp:symbol |
Li₂(z)
|
| gptkbp:usedIn |
gptkb:Hyperbolic_geometry
Feynman diagram calculations |
| gptkbp:bfsParent |
gptkb:Polylogarithm
|
| gptkbp:bfsLayer |
5
|