Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
gptkb:Jonquière's_function
|
| gptkbp:application |
mathematical physics
number theory quantum statistics |
| gptkbp:domain |
complex numbers
|
| gptkbp:generalizes |
dilogarithm
trilogarithm |
| gptkbp:hasSpecialCase |
Riemann zeta function (Li_s(1) = ζ(s))
natural logarithm (Li_1(z) = -ln(1-z)) |
| https://www.w3.org/2000/01/rdf-schema#label |
polylogarithm
|
| gptkbp:introduced |
gptkb:Émile_Léonard_Mathieu
|
| gptkbp:notation |
Li_s(z)
|
| gptkbp:parameter |
z
s |
| gptkbp:relatedTo |
gptkb:Riemann_zeta_function
gptkb:Hurwitz_zeta_function gptkb:Clausen_function multiple zeta values |
| gptkbp:satisfiesFunctionalEquation |
Li_s(z) + (-1)^s Li_s(1/z) = - (2πi)^s / Γ(s) B_s(ln(-z)/2πi)
|
| gptkbp:seriesExpansion |
Li_s(z) = sum_{k=1}^∞ z^k / k^s
|
| gptkbp:bfsParent |
gptkb:Lerch_transcendent
gptkb:Hurwitz_zeta_function |
| gptkbp:bfsLayer |
5
|