DLMF:7.5.E1 (Q2347)

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DLMF:7.5.E1
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    Statements

    Defining formula
    F ⁡ ( z ) = 1 2 ⁢ i ⁢ π ⁢ ( e - z 2 - w ⁡ ( z ) ) = - 1 2 ⁢ i ⁢ π ⁢ e - z 2 ⁢ erf ⁡ ( i ⁢ z ) . Dawsons-integral 𝑧 1 2 𝑖 𝜋 superscript 𝑒 superscript 𝑧 2 error-function-w 𝑧 1 2 𝑖 𝜋 superscript 𝑒 superscript 𝑧 2 error-function 𝑖 𝑧 {\displaystyle{\displaystyle F\left(z\right)=\tfrac{1}{2}i\sqrt{\pi}\left(e^{-% z^{2}}-w\left(z\right)\right)=-\tfrac{1}{2}i\sqrt{\pi}e^{-z^{2}}\operatorname{% erf}\left(iz\right).}}
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    DLMF id
    DLMF:7.5.E1
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    Symbols used
    Dawson’s integral
    Defining formula
    F ⁡ ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E5.m2adec
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    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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    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2adec
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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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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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