DLMF:7.7.E1 (Q2371)

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DLMF:7.7.E1
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    Statements

    Defining formula
    erfc ⁡ z = 2 π ⁢ e - z 2 ⁢ ∫ 0 ∞ e - z 2 ⁢ t 2 t 2 + 1 ⁢ d t , complementary-error-function 𝑧 2 𝜋 superscript 𝑒 superscript 𝑧 2 superscript subscript 0 superscript 𝑒 superscript 𝑧 2 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\pi}e^{-z^{2}}\int_{% 0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\mathrm{d}t,}}
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    DLMF id
    DLMF:7.7.E1
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    constraint
    | ph ⁡ z | ≤ 1 4 ⁢ π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}
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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.m2adec
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    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
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    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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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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