DLMF:1.17.E17 (Q676)

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DLMF:1.17.E17
No description defined

    Statements

    Defining formula
    1 2 ⁢ π ⁢ ∑ k = - ∞ ∞ e - i ⁢ k ⁢ a ⁢ ( ∫ - π π ϕ ⁢ ( x ) ⁢ e i ⁢ k ⁢ x ⁢ d x ) = ϕ ⁢ ( a ) , 1 2 𝜋 superscript subscript 𝑘 superscript 𝑒 𝑖 𝑘 𝑎 superscript subscript 𝜋 𝜋 italic-ϕ 𝑥 superscript 𝑒 𝑖 𝑘 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}% \left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\mathrm{d}x\right)=\phi(a),}}
    0 references
    DLMF id
    DLMF:1.17.E17
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1amdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3amdec
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    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1dec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1fdec
    0 references
     
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