Bessel function

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.23

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https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.23
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.23

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.23

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.23

Designations

ENBessel function

FRfonction de Bessel

Symbol

J_{ν} (z)

Notation systems

AsciiMath

"J"_nu(z)

LaTeX

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

Definition

Bessel function, + cylinder function of the first kind

fonction de Bessel, + fonction cylindrique de première espèce

$J_{ν} (z) = \sum_{k = 0}^{\infty} \frac{{(- 1)}^{k} {(z / 2)}^{ν + 2 k}}{k! Γ (ν + k + 1)}$

(for $ν \in C$ )

Solution of

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

$J_{ν} (z) = \sum_{k = 0}^{\infty} \frac{{(- 1)}^{k} {(z / 2)}^{ν + 2 k}}{k! Γ (ν + k + 1)}$

(pour $ν \in C$ )

Solution de

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

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

isq:t2-20.23

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.23
skosxl:prefLabel	"Bessel function"@en
skosxl:altLabel	""J"_nu(z)"@en
skos:definition	Bessel function, + cylinder function of the first kind
skos:note	stem:["J"_nu(z) = sum_(k=0)^(oo) ((-1)^k(z//2)^(nu+2k))/(k!Gamma(nu+k+1))] (for stem:[nu in bb(sf(C))]) Solution of s…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20