DLMF:3.11.E9 (Q1450)

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DLMF:3.11.E9
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    Statements

    Defining formula
    ∑ ′ ′ ℓ = 0 ′ ′ n ′ ′ ⁢ T j ⁡ ( x ℓ ) ⁢ T k ⁡ ( x ℓ ) = { n , j = k = 0 ⁢  or  ⁢ n , 1 2 ⁢ n , j = k ≠ 0 ⁢  or  ⁢ n , 0 , j ≠ k , superscript subscript superscript fragments ′ ′ ℓ 0 𝑛 Chebyshev-polynomial-first-kind-T 𝑗 subscript 𝑥 ℓ Chebyshev-polynomial-first-kind-T 𝑘 subscript 𝑥 ℓ cases 𝑛 𝑗 𝑘 0  or  𝑛 1 2 𝑛 𝑗 𝑘 0  or  𝑛 0 𝑗 𝑘 {\displaystyle{\displaystyle\sideset{}{{}^{\prime\prime}}{\sum}_{\ell=0}^{n}T_% {j}\left(x_{\ell}\right)T_{k}\left(x_{\ell}\right)=\begin{cases}n,&j=k=0\text{% or }n,\\ \frac{1}{2}n,&j=k\neq 0\text{ or }n,\\ 0,&j\neq k,\end{cases}}}
    0 references
    DLMF id
    DLMF:3.11.E9
    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.m2acdec
    0 references
     
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