DLMF:18.7.E25 (Q5593): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11207 / rank
 
Normal rank
Property / Symbols used: Q11207 / qualifier
 
test:

T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}

\ChebyshevpolyT{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11207 / qualifier
 
xml-id: C18.S3.T1.t1.r4.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11475 / rank
 
Normal rank
Property / Symbols used: Q11475 / qualifier
 
test:

C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11475 / qualifier
 
xml-id: C18.S3.T1.t1.r3.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1xdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1xdec

Latest revision as of 14:22, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.7.E25
No description defined

    Statements

    test
    lim λ → 0 ⁡ 1 λ ⁢ C n ( λ ) ⁡ ( x ) = 2 n ⁢ T n ⁡ ( x ) , subscript → 𝜆 0 1 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 2 𝑛 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\lambda\to 0}\frac{1}{\lambda}C^{(\lambda)}_% {n}\left(x\right)=\frac{2}{n}T_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.7.E25
    0 references
    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
    0 references
    Symbols used
    Q11207
    test
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2acdec
    0 references
    Q11475
    test
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2agdec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1xdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1xdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5593&oldid=31955"