1.17.E10 (Q639)

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1.17.E10
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    Statements

    DLMF defining formula
    1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - t 2 / ( 4 ⁢ n ) ⁢ e i ⁢ ( x - a ) ⁢ t ⁢ d t = n π ⁢ e - n ⁢ ( x - a ) 2 . 1 2 𝜋 superscript subscript superscript 𝑒 superscript 𝑡 2 4 𝑛 superscript 𝑒 𝑖 𝑥 𝑎 𝑡 𝑡 𝑛 𝜋 superscript 𝑒 𝑛 superscript 𝑥 𝑎 2 {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n% )}e^{i(x-a)t}\mathrm{d}t=\sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}.}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1edec
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    Identifiers

     
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