Legendre polynomial

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.15

Download RDF.jsonld .ttl

https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.15
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.15

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.15

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.15

Designations

ENLegendre polynomial

FRpolynôme de Legendre

Symbol

P_{n} (z)

Notation systems

AsciiMath

"P"_n(z)

LaTeX

\text{P}_{n} ( z )

Definition

Legendre polynomial

polynôme de Legendre

$P_{n} (z) = \frac{1}{2^{n} n!} \frac{d^{n}}{d z^{n}} {(z^{2} - 1)}^{n}$

(for $n \in N$ )

Solution of

$(1 - z^{2}) y ″ - 2 z y' + n (n + 1) y = 0$

$P_{n} (z) = \frac{1}{2^{n} n!} \frac{d^{n}}{d z^{n}} {(z^{2} - 1)}^{n}$

(pour $n \in N$ )

Solution de

$(1 - z^{2}) y ″ - 2 z y' + n (n + 1) y = 0$

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

isq:t2-20.15

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.15
skosxl:prefLabel	"Legendre polynomial"@en
skosxl:altLabel	""P"_n(z)"@en
skos:definition	Legendre polynomial
skos:note	stem:["P"_n(z) = 1/(2^n n!) ("d"^n)/("d"z^n) (z^2-1)^n] (for stem:[n in bb(sf(N))]) Solution of stem:[(1-z^2)y'' - 2z…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20