Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
gptkb:Lerch_zeta_function
|
| gptkbp:appearsIn |
mathematical physics
analytic number theory |
| gptkbp:definedIn |
Φ(z, s, a) = Σ_{n=0}^∞ z^n / (n + a)^s
|
| gptkbp:differentiableWithRespectTo |
a
z s |
| gptkbp:domain |
|z| < 1 or (|z| = 1 and Re(s) > 1)
|
| gptkbp:generalizes |
gptkb:Hurwitz_zeta_function
gptkb:polylogarithm |
| gptkbp:hasSeriesExpansion |
Σ_{n=0}^∞ z^n / (n + a)^s
|
| gptkbp:hasSpecialCase |
Hurwitz zeta function when z=1
polylogarithm when a=1 |
| https://www.w3.org/2000/01/rdf-schema#label |
Lerch transcendent
|
| gptkbp:namedAfter |
gptkb:Mathias_Lerch
|
| gptkbp:symbol |
Φ(z, s, a)
|
| gptkbp:usedIn |
modular forms
quantum statistics partition functions |
| gptkbp:variant |
a
z s |
| gptkbp:bfsParent |
gptkb:lion
|
| gptkbp:bfsLayer |
4
|