DLMF:18.18.E31 (Q5821)

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DLMF:18.18.E31
No description defined

    Statements

    Defining formula
    ∑ ℓ = 0 n T ℓ ⁡ ( x ) ⁢ x n - ℓ = U n ⁡ ( x ) . superscript subscript ℓ 0 𝑛 Chebyshev-polynomial-first-kind-T ℓ 𝑥 superscript 𝑥 𝑛 ℓ Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}T_{\ell}\left(x\right)x^{n-\ell}=% U_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E31
    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.m2aadec
    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.m2adec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1rdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1addec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1zdec
    0 references
     
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