DLMF:3.5.E39 (Q1294)

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DLMF:3.5.E39
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    Statements

    Defining formula
    g ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ ∫ σ - i ⁢ ∞ σ + i ⁢ ∞ e t ⁢ p ⁢ G ⁢ ( p ) ⁢ d p , 𝑔 𝑡 1 2 imaginary-unit superscript subscript 𝜎 imaginary-unit 𝜎 imaginary-unit superscript 𝑒 𝑡 𝑝 𝐺 𝑝 𝑝 {\displaystyle{\displaystyle g(t)=\frac{1}{2\pi\mathrm{i}}\int_{\sigma-\mathrm% {i}\infty}^{\sigma+\mathrm{i}\infty}e^{tp}G(p)\mathrm{d}p,}}
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    DLMF id
    DLMF:3.5.E39
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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.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
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