DLMF:18.33.E1 (Q6007)

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DLMF:18.33.E1
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ i ⁢ ∫ | z | = 1 ϕ n ⁢ ( z ) ⁢ ϕ m ⁢ ( z ) ¯ ⁢ w ⁢ ( z ) ⁢ d z z = δ n , m , 1 2 𝜋 imaginary-unit subscript 𝑧 1 subscript italic-ϕ 𝑛 𝑧 subscript italic-ϕ 𝑚 𝑧 𝑤 𝑧 𝑧 𝑧 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{|z|=1}\phi_{n}(z)% \overline{\phi_{m}(z)}w(z)\frac{\mathrm{d}z}{z}=\delta_{n,m},}}
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    DLMF id
    DLMF:18.33.E1
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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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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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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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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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