DLMF:7.8.E1 (Q2387)

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DLMF:7.8.E1
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    Statements

    Defining formula
    𝖬 ⁡ ( x ) = ∫ x ∞ e - t 2 ⁢ d t e - x 2 = e x 2 ⁢ ∫ x ∞ e - t 2 ⁢ d t . Mills-ratio 𝑥 superscript subscript 𝑥 superscript 𝑒 superscript 𝑡 2 𝑡 superscript 𝑒 superscript 𝑥 2 superscript 𝑒 superscript 𝑥 2 superscript subscript 𝑥 superscript 𝑒 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathsf{M}\left(x\right)=\frac{\int_{x}^{\infty}e^% {-t^{2}}\mathrm{d}t}{e^{-x^{2}}}=e^{x^{2}}\int_{x}^{\infty}e^{-t^{2}}\mathrm{d% }t.}}
    0 references
    DLMF id
    DLMF:7.8.E1
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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