hypergeometric function

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.13

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https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.13
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.13

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.13

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.13

Designations

ENhypergeometric function

FRfonction hypergéométrique

Symbol

F (a, b, c; z)

Notation systems

AsciiMath

"F"(a,b,c;z)

LaTeX

\text{F} ( a , b , c ; z )

Definition

hypergeometric function

fonction hypergéométrique

Notes

$F (a, b, c; z) = \sum_{n = 0}^{\infty} \frac{{(a)}_{n} {(b)}_{n} z^{n}}{{(c)}_{n} n!}$

(for $- c \notin N$ )

For ${(a)}_{n}$ , ${(b)}_{n}$ and ${(c)}_{n}$ , see rising factorial.

Solution of

$z (1 - z) y ″ + [c - (a + b + 1) z \$ y' - aby = 0]

$F (a, b, c; z) = \sum_{n = 0}^{\infty} \frac{{(a)}_{n} {(b)}_{n} z^{n}}{{(c)}_{n} n!}$

(pour $- c \notin N$ )

Pour ${(a)}_{n}$ , ${(b)}_{n}$ et ${(c)}_{n}$ , voir rising factorial.

Solution de

$z (1 - z) y ″ + [c - (a + b + 1) z \$ y' - aby = 0]

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:t2-20.13

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.13
skosxl:prefLabel	"hypergeometric function"@en
skosxl:altLabel	""F"(a,b,c;z)"@en
skos:definition	hypergeometric function
skos:note	stem:[F(a,b,c;z) = sum_(n=0)^(oo) ((a)_n (b)_n z^n)/((c)_n n!)] (for stem:[-c !in bb(sf(N))]) For stem:[(a)_n], stem:[…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20

Related Entities

isq:MathConceptShape isq:part-2-20 smart:TermEntry