DLMF:6.7.E6 (Q2259)

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DLMF:6.7.E6
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    Statements

    test
    ∫ x ∞ t ⁢ e - t a 2 + t 2 ⁢ d t = 1 2 ⁢ ( e i ⁢ a ⁢ E 1 ⁡ ( x + i ⁢ a ) + e - i ⁢ a ⁢ E 1 ⁡ ( x - i ⁢ a ) ) , superscript subscript 𝑥 𝑡 superscript 𝑒 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}% \mathrm{d}t=\tfrac{1}{2}\left(e^{ia}E_{1}\left(x+ia\right)+e^{-ia}E_{1}\left(x% -ia\right)\right),}}
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    DLMF id
    DLMF:6.7.E6
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    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
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    x ∈ ℝ 𝑥 ℝ {\displaystyle{\displaystyle x\in\mathbb{R}}}
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