DLMF:30.15.E8 (Q8950)

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DLMF:30.15.E8
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    Statements

    Defining formula
    ∫ - ∞ ∞ ϕ k ⁢ ( t ) ⁢ ϕ n ⁢ ( t ) ⁢ d t = δ k , n . superscript subscript subscript italic-ϕ 𝑘 𝑡 subscript italic-ϕ 𝑛 𝑡 𝑡 Kronecker 𝑘 𝑛 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\phi_{k}(t)\phi_{n}(t)% \mathrm{d}t=\delta_{k,n}.}}
    0 references
    DLMF id
    DLMF:30.15.E8
    0 references
    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.m5aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1fdec
    0 references
    function (locally)
    Defining formula
    ϕ n ⁢ ( t ) subscript italic-ϕ 𝑛 𝑡 {\displaystyle{\displaystyle\phi_{n}(t)}}
    xml-id
    C30.S15.XMD3.m1edec
    0 references
     
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