DLMF:1.17.E9 (Q668)

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DLMF:1.17.E9
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    Statements

    Defining formula
    ∫ - ∞ ∞ ( 1 2 ⁢ π ⁢ ∫ - ∞ ∞ e i ⁢ ( x - a ) ⁢ t ⁢ d t ) ⁢ ϕ ⁢ ( x ) ⁢ d x = ϕ ⁢ ( a ) . superscript subscript 1 2 𝜋 superscript subscript superscript 𝑒 𝑖 𝑥 𝑎 𝑡 𝑡 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-% \infty}^{\infty}e^{i(x-a)t}\mathrm{d}t\right)\phi(x)\mathrm{d}x=\phi(a).}}
    0 references
    DLMF id
    DLMF:1.17.E9
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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.m2addec
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