beta function

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.4

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https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.4
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.4

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.4

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.4

Designations

ENbeta function

FRfonction bêta

Symbol

B (z, w)

Notation systems

AsciiMath

"B"(z,w)

LaTeX

\text{B} ( z , w )

Definition

beta function

fonction bêta

$B (z, w) = \int_{0}^{1} t^{z - 1} {(1 - t)}^{w - 1} d t$

(for $Re z > 0$ , $Re w > 0$ )

$B (z, w) = Γ (z) Γ (w) / Γ (z + w)$

$\frac{1}{(n + 1) B (k + 1, n - k + 1)} = (\begin{matrix} n \\ k \end{matrix})$ (for $k \leq n$ )

$B (z, w) = \int_{0}^{1} t^{z - 1} {(1 - t)}^{w - 1} d t$

(pour $Re z > 0$ , $Re w > 0$ )

$B (z, w) = Γ (z) Γ (w) / Γ (z + w)$

$\frac{1}{(n + 1) B (k + 1, n - k + 1)} = (\begin{matrix} n \\ k \end{matrix})$ (pour $k \leq n$ )

A mathematical concept as defined in ISO/IEC 80000 Part 2.

isq:t2-20.4

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.4
skosxl:prefLabel	"beta function"@en
skosxl:altLabel	""B"(z,w)"@en
skos:definition	beta function
skos:note	stem:["B"(z,w) = int_0^1 t^(z-1)(1-t)^(w-1) "d"t] (for stem:["Re "z > 0], stem:["Re "w > 0]) stem:[rm(B)(z,w) = Gamma(…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20