Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Lerch_transcendent
|
| gptkbp:appearsIn |
gptkb:Analytic_number_theory
Mathematical physics |
| gptkbp:definedIn |
Φ(z,s,a) = Σ_{n=0}^∞ z^n / (n+a)^s
|
| gptkbp:domain |
gptkb:Complex_numbers
|
| gptkbp:firstDescribed |
1887
|
| gptkbp:generalizes |
gptkb:Hurwitz_zeta_function
gptkb:Polylogarithm |
| gptkbp:hasIntegralRepresentation |
Yes
|
| gptkbp:hasSeriesExpansion |
Σ_{n=0}^∞ z^n / (n+a)^s
|
| gptkbp:hasSingularityAt |
a=0
|
| gptkbp:hasSpecialCase |
gptkb:Riemann_zeta_function
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lerch zeta function
|
| gptkbp:isAnalyticIn |
z≠1 or Re(s)>1
|
| gptkbp:isMeromorphic |
Yes
|
| gptkbp:namedAfter |
gptkb:Mathias_Lerch
|
| gptkbp:usedIn |
gptkb:Special_functions_theory
Quantum statistics |
| gptkbp:variant |
a
z s |
| gptkbp:bfsParent |
gptkb:lion
|
| gptkbp:bfsLayer |
4
|