DLMF:18.18.E34 (Q5824): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11207 / rank
 
Normal rank
Property / Symbols used: Q11207 / qualifier
 
Defining formula:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11661 / rank
 
Normal rank
Property / Symbols used: Q11661 / qualifier
 
Defining formula:

U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}

\ChebyshevpolyU{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11661 / qualifier
 
xml-id: C18.S3.T1.t1.r5.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
Defining formula:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.m1udec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1agdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1acdec

Latest revision as of 01:28, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.18.E34
No description defined

    Statements

    Defining formula
    2 ⁢ ( 1 - x 2 ) ⁢ ∑ ℓ = 0 n U 2 ⁢ ℓ ⁡ ( x ) = 1 - T 2 ⁢ n + 2 ⁡ ( x ) , 2 1 superscript 𝑥 2 superscript subscript ℓ 0 𝑛 Chebyshev-polynomial-second-kind-U 2 ℓ 𝑥 1 Chebyshev-polynomial-first-kind-T 2 𝑛 2 𝑥 {\displaystyle{\displaystyle 2(1-x^{2})\sum_{\ell=0}^{n}U_{2\ell}\left(x\right% )=1-T_{2n+2}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.18.E34
    0 references
    Symbols used
    Q11207
    Defining formula
    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.m2addec
    0 references
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2acdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1udec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1agdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1acdec
    0 references
     
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