DLMF:4.10.E11 (Q1626)

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DLMF:4.10.E11
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    Statements

    Defining formula
    ∫ - ∞ ∞ e - c ⁢ x 2 ⁢ d x = π c , superscript subscript superscript 𝑒 𝑐 superscript 𝑥 2 𝑥 𝜋 𝑐 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{-cx^{2}}\mathrm{d}x=% \sqrt{\frac{\pi}{c}},}}
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    DLMF id
    DLMF:4.10.E11
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    constraint
    ℜ ⁡ c > 0 𝑐 0 {\displaystyle{\displaystyle\Re c>0}}
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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.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
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