DLMF:7.7.E2 (Q2372)

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DLMF:7.7.E2
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    Statements

    Defining formula
    w ⁡ ( z ) = 1 π ⁢ i ⁢ ∫ - ∞ ∞ e - t 2 ⁢ d t t - z = 2 ⁢ z π ⁢ i ⁢ ∫ 0 ∞ e - t 2 ⁢ d t t 2 - z 2 , error-function-w 𝑧 1 𝜋 𝑖 superscript subscript superscript 𝑒 superscript 𝑡 2 𝑡 𝑡 𝑧 2 𝑧 𝜋 𝑖 superscript subscript 0 superscript 𝑒 superscript 𝑡 2 𝑡 superscript 𝑡 2 superscript 𝑧 2 {\displaystyle{\displaystyle w\left(z\right)=\frac{1}{\pi i}\int_{-\infty}^{% \infty}\frac{e^{-t^{2}}\mathrm{d}t}{t-z}=\frac{2z}{\pi i}\int_{0}^{\infty}% \frac{e^{-t^{2}}\mathrm{d}t}{t^{2}-z^{2}},}}
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    DLMF id
    DLMF:7.7.E2
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    constraint
    ℑ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Im z>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.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    Faddeeva (or Faddeyeva) function
    Defining formula
    w ⁡ ( z ) error-function-w 𝑧 {\displaystyle{\displaystyle w\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E3.m2adec
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