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Section 2-119 entries

2-11.1factorial 2-11.2falling factorial 2-11.3rising factorial 2-11.4binomial coefficient 2-11.5Bernoulli numbers 2-11.6number of combinations without repetition 2-11.7number of combinations with repetition 2-11.8number of variations without repetition 2-11.9number of variations with repetition

2-11.3

rising factorial

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-11.3

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/math/part-2-11/t2-11.3
urn:iso:std:iso:80000:-2:ed-2:en:item:2-11.3

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-11.3

IEC

urn:iec:std:iec:80000-2:2019:::item:2-11.3

Designations

ENrising factorial

FRfactorielle croissante

Symbol

a^{\bar{k}}

Notation systems

AsciiMath

a^(bar(k))

LaTeX

a^{\overline{k}}

Definition

rising factorial

factorielle croissante + factorielle montante

Notes

$a^{\bar{k}} = a \cdot (a + 1) \cdot \dots \cdot (a + k - 1)$ (for $k > 0$ )

$a^{\bar{0}} = 1$

$a$ may be a complex number.

For a natural number $n$ :

$n^{\bar{k}} = \frac{(n + k - 1)!}{(n - 1)!}$

In the theory of special functions, the symbol ${(a)}_{k}$ is often used for the rising factorial and called Pochhammer symbol. In combinatorics and statistics, however, the same symbol is often used for the falling factorial.

$a^{\bar{k}} = a \cdot (a + 1) \cdot \dots \cdot (a + k - 1)$ (pour $k > 0$ )

$a^{\bar{0}} = 1$

$a$ peut être un nombre complexe.

Pour tout entier naturel $n$ :

$n^{\bar{k}} = \frac{(n + k - 1)!}{(n - 1)!}$

Dans la théorie des fonctions spéciales, le symbole ${(a)}_{k}$ est souvent utilisé pour les factorielles croissantes et est appelé symbole de Pochhammer. En combinatoire et en statistique cependant, le même symbole est souvent utilisé pour les factorielles décroissantes.

Referenced by

hypergeometric function confluent hypergeometric function

Ontology
isq:MathConcept smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:MathConcept

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

Instance IRI

isq:t2-11.3

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-11.3
skosxl:prefLabel	"rising factorial"@en
skosxl:altLabel	"a^(bar(k))"@en
skos:definition	rising factorial
skos:note	stem:[a^(bar(k)) = a (a + 1) ... *(a + k - 1)] (for stem:[k > 0]) stem:[a^(bar(0)) = 1] stem:[a] may be a complex nu…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-11

Related Entities

isq:MathConceptShape isq:part-2-11 smart:TermEntry