DLMF:7.2.E3 (Q2323)

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DLMF:7.2.E3
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    Defining formula
    w ⁡ ( z ) = e - z 2 ⁢ ( 1 + 2 ⁢ i π ⁢ ∫ 0 z e t 2 ⁢ d t ) = e - z 2 ⁢ erfc ⁡ ( - i ⁢ z ) . error-function-w 𝑧 superscript 𝑒 superscript 𝑧 2 1 2 𝑖 𝜋 superscript subscript 0 𝑧 superscript 𝑒 superscript 𝑡 2 𝑡 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑖 𝑧 {\displaystyle{\displaystyle{}w\left(z\right)=e^{-z^{2}}\left(1+\frac{2i}{% \sqrt{\pi}}\int_{0}^{z}e^{t^{2}}\mathrm{d}t\right)=e^{-z^{2}}\operatorname{% erfc}\left(-iz\right).}}
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    DLMF:7.2.E3
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