DLMF:3.11.E37 (Q1485)

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DLMF:3.11.E37
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    Statements

    Defining formula
    ∑ j = 0 n - 1 ϕ k ⁢ ( x j ) ⁢ ϕ ℓ ⁢ ( x j ) ¯ = n ⁢ δ k , ℓ , superscript subscript 𝑗 0 𝑛 1 subscript italic-ϕ 𝑘 subscript 𝑥 𝑗 subscript italic-ϕ ℓ subscript 𝑥 𝑗 𝑛 Kronecker 𝑘 ℓ {\displaystyle{\displaystyle\sum_{j=0}^{n-1}\phi_{k}(x_{j})\overline{\phi_{% \ell}(x_{j})}=n\delta_{k,\ell},}}
    0 references
    DLMF id
    DLMF:3.11.E37
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    constraint
    k , ℓ = 0 , 1 , … , n - 1 formulae-sequence 𝑘 ℓ 0 1 … 𝑛 1 {\displaystyle{\displaystyle k,\ell=0,1,\dots,n-1}}
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    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
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    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
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    Q11215
    Defining formula
    ϕ k ⁢ ( x ) subscript italic-ϕ 𝑘 𝑥 {\displaystyle{\displaystyle\phi_{k}(x)}}
    xml-id
    C3.S11.XMD19.m1ddec
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