Chebyshev polynomial of the second kind

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.22

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https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.22
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.22

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.22

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.22

Designations

ENChebyshev polynomial of the second kind

FRpolynôme de Chebyshev de deuxième espèce

Symbol

U_{n} (z)

Notation systems

AsciiMath

"U"_n(z)

LaTeX

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

Definition

Chebyshev polynomial of the second kind

polynôme de Chebyshev de deuxième espèce

$U_{n} (z) = (sin [(n + 1) arccos z \$ )/("sin"("arccos"z))]

(for $n \in N$ )

Solution of

$(1 - z^{2}) y ″ - 3 z y' + n (n + 2) y = 0$

$U_{n} (z) = (sin [(n + 1) arccos z \$ )/("sin"("arccos"z))]

(pour $n \in N$ )

Solution de

$(1 - z^{2}) y ″ - 3 z y' + n (n + 2) y = 0$

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

isq:t2-20.22

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.22
skosxl:prefLabel	"Chebyshev polynomial of the second kind"@en
skosxl:altLabel	""U"_n(z)"@en
skos:definition	Chebyshev polynomial of the second kind
skos:note	stem:["U"_n(z) = ("sin"[(n+1)"arccos"z\])/("sin"("arccos"z))] (for stem:[n in bb(sf(N))]) Solution of stem:[(1-z^2)y'…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20