Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:gamma_function
|
| gptkbp:definedIn |
Γ(z) = ∫₀^∞ t^{z-1} e^{-t} dt
|
| gptkbp:domain |
complex numbers except non-positive integers
|
| gptkbp:firstPublished |
1729
|
| gptkbp:generalizes |
factorial function
|
| gptkbp:hasEquation |
Γ(z+1) = zΓ(z)
|
| gptkbp:hasPolesAt |
non-positive integers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euler's gamma function
|
| gptkbp:introduced |
gptkb:Leonhard_Euler
|
| gptkbp:isAnalyticExceptAt |
non-positive integers
|
| gptkbp:isMeromorphic |
true
|
| gptkbp:relatedTo |
gptkb:digamma_function
gptkb:Riemann_zeta_function beta function |
| gptkbp:satisfies |
Γ(n) = (n-1)!
|
| gptkbp:symbol |
Γ(z)
|
| gptkbp:usedIn |
gptkb:probability_theory
complex analysis number theory physics statistics |
| gptkbp:valueAt |
Γ(1) = 1
Γ(1/2) = √π |
| gptkbp:bfsParent |
gptkb:gamma_function
|
| gptkbp:bfsLayer |
6
|