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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

2-20.26

modified Bessel function

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.26

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.26
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.26

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.26

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.26

Designations

ENmodified Bessel function

FRfonction de Bessel modifiée

Symbol

I_{ν} (z)

K_{ν} (z)

Notation systems

AsciiMath

"I"_nu(z)

AsciiMath

"K"_nu(z)

LaTeX

\text{I}_{\nu} ( z )

LaTeX

\text{K}_{\nu} ( z )

Definition

modified Bessel function

fonction de Bessel modifiée

Notes

$I_{ν} (z) = e^{- 1 / 2 i ν π} J_{ν} (e^{1 / 2 i π_{Z}})$

$K_{ν} (z) = \frac{i π}{2} e^{1 / 2 ν π} H_{ν}^{(1)} (e^{1 / 2 i π_{Z}})$

(for $ν \in C$ )

Solution of $z^{2} y ″ + z y' - (z^{2} + ν^{2}) y = 0$

$I_{ν} (z) = e^{- 1 / 2 i ν π} J_{ν} (e^{1 / 2 i π_{Z}})$

$K_{ν} (z) = \frac{i π}{2} e^{1 / 2 ν π} H_{ν}^{(1)} (e^{1 / 2 i π_{Z}})$

(pour $ν \in C$ )

Solution de $z^{2} y ″ + z y' - (z^{2} + ν^{2}) y = 0$

Referenced by

spherical Hankel 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:t2-20.26

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.26
skosxl:prefLabel	"modified Bessel function"@en
skosxl:altLabel	""I"_nu(z)"@en""K"_nu(z)"@en
skos:definition	modified Bessel function
skos:note	stem:["I"_nu (z) = "e"^(-1//2 "i"nu pi)"J"_nu ("e"^(1//2 "i"pi_Z))] stem:["K"_nu (z) = ("i"pi)/2 "e"^(1//2 nu pi) "H"_n…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20

Related Entities

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