DLMF:18.18.E35 (Q5825): Difference between revisions

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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.m1addec

Latest revision as of 01:28, 2 January 2020

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DLMF:18.18.E35
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    Statements

    Defining formula
    2 ⁢ ( 1 - x 2 ) ⁢ ∑ ℓ = 0 n U 2 ⁢ ℓ + 1 ⁡ ( x ) = x - T 2 ⁢ n + 3 ⁡ ( x ) . 2 1 superscript 𝑥 2 superscript subscript ℓ 0 𝑛 Chebyshev-polynomial-second-kind-U 2 ℓ 1 𝑥 𝑥 Chebyshev-polynomial-first-kind-T 2 𝑛 3 𝑥 {\displaystyle{\displaystyle 2(1-x^{2})\sum_{\ell=0}^{n}U_{2\ell+1}\left(x% \right)=x-T_{2n+3}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E35
    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.m2aedec
    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.m2addec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1vdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ahdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1addec
    0 references
     
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