Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
beta function
|
| gptkbp:category |
integral transforms
|
| gptkbp:definedIn |
B(x, y) = ∫₀¹ t^{x-1} (1-t)^{y-1} dt
|
| gptkbp:domain |
Re(x) > 0, Re(y) > 0
|
| gptkbp:hasIntegralRepresentation |
B(x, y) = ∫₀^∞ t^{x-1} / (1+t)^{x+y} dt
|
| gptkbp:hasSeriesRepresentation |
B(x, y) = Σ_{n=0}^∞ [(1-y)_n / (n! (x+n))]
|
| gptkbp:hasSpecialCase |
B(1, y) = 1/y
B(x, 1) = 1/x |
| https://www.w3.org/2000/01/rdf-schema#label |
Euler beta function
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:relatedTo |
gptkb:gamma_function
|
| gptkbp:relationToGammaFunction |
B(x, y) = Γ(x)Γ(y)/Γ(x+y)
|
| gptkbp:symbol |
B(x, y)
|
| gptkbp:symmetry |
B(x, y) = B(y, x)
|
| gptkbp:usedIn |
gptkb:mathematics
gptkb:probability_theory calculus physics statistics combinatorics |
| gptkbp:bfsParent |
gptkb:Veneziano_amplitude
|
| gptkbp:bfsLayer |
7
|