DLMF:6.7.E1 (Q2254)

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DLMF:6.7.E1
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t t + b ⁢ d t = ∫ 0 ∞ e i ⁢ a ⁢ t t + i ⁢ b ⁢ d t = e a ⁢ b ⁢ E 1 ⁡ ( a ⁢ b ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 𝑡 𝑏 𝑡 superscript subscript 0 superscript 𝑒 𝑖 𝑎 𝑡 𝑡 𝑖 𝑏 𝑡 superscript 𝑒 𝑎 𝑏 exponential-integral 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{t+b}\mathrm{d}t=% \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\mathrm{d}t=e^{ab}E_{1}\left(ab\right),}}
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    DLMF:6.7.E1
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