spherical harmonic

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.17

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.17
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.17

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.17

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.17

Designations

ENspherical harmonic

FRharmonique sphérique

Symbol

Y_{l}^{m} (ϑ, φ)

Notation systems

AsciiMath

"Y"_l^m(vartheta,varphi)

LaTeX

\text{Y}_{l}^{m} ( \vartheta , \varphi )

Definition

spherical harmonic

harmonique sphérique

Notes

$Y_{l}^{m} (ϑ, φ) = [(\frac{2 l + 1}{4 π}) \frac{(l - | m |)!}{(l + | m |)!} \$ ^(1//2) P_l^(abs m) ("cos" vartheta)"e"^("i" m varphi)]

(for $l, | m | \in N; | m | \leq l$ )

Solution of

$\frac{1}{sin ϑ} \frac{\partial}{\partial ϑ} (\sin ϑ \frac{\partial y}{\partial ϑ}) + \frac{1}{{sin}^{2} ϑ} \frac{\partial^{2} y}{\partial φ^{2}} + l (l + 1) y = 0$

$Y_{l}^{m} (ϑ, φ) = [(\frac{2 l + 1}{4 π}) \frac{(l - | m |)!}{(l + | m |)!} \$ ^(1//2) P_l^(abs m) ("cos" vartheta)"e"^("i" m varphi)]

(pour $l, | m | \in N; | m | \leq l$ )

Solution de

$\frac{1}{sin ϑ} \frac{\partial}{\partial ϑ} (\sin ϑ \frac{\partial y}{\partial ϑ}) + \frac{1}{{sin}^{2} ϑ} \frac{\partial^{2} y}{\partial φ^{2}} + l (l + 1) y = 0$

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:t2-20.17

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.17
skosxl:prefLabel	"spherical harmonic"@en
skosxl:altLabel	""Y"_l^m(vartheta,varphi)"@en
skos:definition	spherical harmonic
skos:note	stem:["Y"_l^m(vartheta, varphi) = [((2l+1)/(4pi)) ((l-abs m)!)/((l+ abs m)!)\]^(1//2) P_l^(abs m) ("cos" vartheta)"e"^("…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20

Related Entities

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