Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
psi function
|
| gptkbp:application |
calculus
number theory physics statistics |
| gptkbp:asymptoticExpansion |
ψ(x) ~ ln x - 1/(2x) for large x
|
| gptkbp:definedIn |
the logarithmic derivative of the gamma function
|
| gptkbp:differential |
ψ'(x) = ∑_{n=0}^∞ 1/(x+n)^2
|
| gptkbp:domain |
complex numbers except non-positive integers
|
| gptkbp:form |
ψ(x) = d/dx ln Γ(x)
|
| gptkbp:hasSpecialCase |
ψ(1) = -γ (Euler–Mascheroni constant)
|
| https://www.w3.org/2000/01/rdf-schema#label |
digamma function
|
| gptkbp:integration |
ψ(x) = ∫₀^∞ (e^{-t} - e^{-xt})/(1 - e^{-t}) dt
|
| gptkbp:inverseFunction |
no elementary inverse
|
| gptkbp:recurrence |
ψ(x+1) = ψ(x) + 1/x
|
| gptkbp:relatedTo |
gptkb:gamma_function
gptkb:polygamma_function |
| gptkbp:seriesExpansion |
ψ(x) = ln x - 1/(2x) - ∑_{k=1}^∞ B_{2k}/(2k x^{2k})
|
| gptkbp:symbol |
ψ(x)
|
| gptkbp:valueAtHalf |
ψ(1/2) = -2ln2 - γ
|
| gptkbp:bfsParent |
gptkb:gamma_function
gptkb:Euler–Mascheroni_constant |
| gptkbp:bfsLayer |
6
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