Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Special function
|
| gptkbp:alsoKnownAs |
Polylogarithm of order 3
|
| gptkbp:analyticContinuation |
Yes
|
| gptkbp:appearsIn |
gptkb:Algebraic_K-theory
gptkb:quantum_field_theory gptkb:Number_theory |
| gptkbp:definedIn |
Li₃(z) = ∑_{k=1}^∞ z^k / k^3
|
| gptkbp:differentiationFormula |
d/dz Li₃(z) = Li₂(z)/z
|
| gptkbp:domain |
gptkb:Complex_numbers
|
| gptkbp:generalizes |
gptkb:Dilogarithm
Logarithm |
| gptkbp:hasSpecialCase |
Li₃(-1) = -3/8 ζ(3)
Li₃(0) = 0 Li₃(1) = ζ(3) |
| https://www.w3.org/2000/01/rdf-schema#label |
Trilogarithm
|
| gptkbp:inverseFunction |
No
|
| gptkbp:notation |
Li₃(z)
|
| gptkbp:relatedTo |
gptkb:Polylogarithm
gptkb:Dilogarithm |
| gptkbp:satisfies |
Functional equations
|
| gptkbp:seriesExpansion |
Li₃(z) = z + z²/8 + z³/27 + ...
|
| gptkbp:bfsParent |
gptkb:Polylogarithm
|
| gptkbp:bfsLayer |
5
|