Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
psi function
|
| gptkbp:analytic |
yes, except at non-positive integers
|
| gptkbp:application |
gptkb:quantum_physics
calculus number theory statistics |
| gptkbp:definedIn |
the logarithmic derivative of the gamma function
|
| gptkbp:differentiable |
yes
|
| gptkbp:domain |
complex numbers except non-positive integers
|
| gptkbp:form |
ψ(x) = d/dx ln(Γ(x))
|
| gptkbp:hasAsymptoticExpansion |
ψ(x) ~ ln(x) - 1/(2x) for large x
|
| gptkbp:hasReflectionFormula |
ψ(1-x) - ψ(x) = π cot(πx)
|
| gptkbp:hasSeriesExpansion |
ψ(x) = ln(x) - 1/(2x) - ∑_{k=1}^∞ B_{2k}/(2k x^{2k})
|
| https://www.w3.org/2000/01/rdf-schema#label |
Digamma function
|
| gptkbp:isPolygammaOfOrder |
0
|
| gptkbp:recurrence |
ψ(x+1) = ψ(x) + 1/x
|
| gptkbp:relatedTo |
gptkb:gamma_function
gptkb:polygamma_function |
| gptkbp:symbol |
ψ(x)
|
| gptkbp:valueAt1 |
-γ (Euler-Mascheroni constant)
|
| gptkbp:bfsParent |
gptkb:Gamma_function
|
| gptkbp:bfsLayer |
6
|