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Section 2-2030 entries

2-20.1Euler-Mascheroni constant 2-20.2gamma function 2-20.3Riemann zeta function 2-20.4beta function 2-20.5exponential integral 2-20.6logarithmic integral 2-20.7sine integral 2-20.8Fresnel integral 2-20.9error function 2-20.10incomplete elliptic integral of the first kind 2-20.11incomplete elliptic integral of the second kind 2-20.12incomplete elliptic integral of the third kind 2-20.13hypergeometric function 2-20.14confluent hypergeometric function 2-20.15Legendre polynomial 2-20.16associated Legendre function 2-20.17spherical harmonic 2-20.18Hermite polynomial 2-20.19Laguerre polynomial 2-20.20associated Laguerre polynomial 2-20.21Chebyshev polynomial of the first kind 2-20.22Chebyshev polynomial of the second kind 2-20.23Bessel function 2-20.24Neumann function 2-20.25Hankel function 2-20.26modified Bessel function 2-20.27spherical Bessel function 2-20.28spherical Neumann function 2-20.29spherical Hankel function 2-20.30Airy function

2-20.30

Airy function

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.30

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.30
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.30

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.30

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.30

Designations

ENAiry function

FRfonction d'Airy

Symbol

Ai (z)

Bi (z)

Notation systems

AsciiMath

"Ai"(z)

AsciiMath

"Bi"(z)

LaTeX

\text{Ai} ( z )

LaTeX

\text{Bi} ( z )

Definition

Airy function

fonction d'Airy

Notes

$Ai (z) = \frac{1}{3} \sqrt{z} [I_{- \frac{1}{3}} (w) - I_{\frac{1}{3}} (w) \$ ]

$Bi (z) = \sqrt{\frac{z}{3}} [I_{- \frac{1}{3}} (w) + I_{\frac{1}{3}} (w) \$ ]

where $w = \frac{2}{3} z^{3 / 2}$ .

Entire solution of $y ″ - z y = 0$

$Ai (z) = \frac{1}{3} \sqrt{z} [I_{- \frac{1}{3}} (w) - I_{\frac{1}{3}} (w) \$ ]

$Bi (z) = \sqrt{\frac{z}{3}} [I_{- \frac{1}{3}} (w) + I_{\frac{1}{3}} (w) \$ ]

où $w = \frac{2}{3} z^{3 / 2}$ .

Solution entière de $y ″ - z y = 0$

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:t2-20.30

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.30
skosxl:prefLabel	"Airy function"@en
skosxl:altLabel	""Ai"(z)"@en""Bi"(z)"@en
skos:definition	Airy function
skos:note	stem:["Ai"(z) = 1/3 sqrt(z) ["I"_(-1/3)(w) - "I"_(1/3)(w)\]] stem:["Bi"(z) = sqrt(z/3) ["I"_(-1/3)(w) + "I"_(1/3)(w)\]]…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20

Related Entities

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