DLMF:7.7.E3 (Q2373)

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DLMF:7.7.E3
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    test
    ∫ 0 ∞ e - a ⁢ t 2 + 2 ⁢ i ⁢ z ⁢ t ⁢ d t = 1 2 ⁢ π a ⁢ e - z 2 / a + i a ⁢ F ⁡ ( z a ) , superscript subscript 0 superscript 𝑒 𝑎 superscript 𝑡 2 2 𝑖 𝑧 𝑡 𝑡 1 2 𝜋 𝑎 superscript 𝑒 superscript 𝑧 2 𝑎 𝑖 𝑎 Dawsons-integral 𝑧 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at^{2}+2izt}\mathrm{d}t=\frac% {1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}F\left(\frac{z}{\sqrt% {a}}\right),}}
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    DLMF:7.7.E3
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