DLMF:6.7.E3 (Q2256)

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DLMF:6.7.E3
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    Defining formula
    ∫ x ∞ e i ⁢ t a 2 + t 2 ⁢ d t = i 2 ⁢ a ⁢ ( e a ⁢ E 1 ⁡ ( a - i ⁢ x ) - e - a ⁢ E 1 ⁡ ( - a - i ⁢ x ) ) , superscript subscript 𝑥 superscript 𝑒 𝑖 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 𝑖 2 𝑎 superscript 𝑒 𝑎 exponential-integral 𝑎 𝑖 𝑥 superscript 𝑒 𝑎 exponential-integral 𝑎 𝑖 𝑥 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{e^{it}}{a^{2}+t^{2}}\mathrm% {d}t=\frac{i}{2a}\left(e^{a}E_{1}\left(a-ix\right)-e^{-a}E_{1}\left(-a-ix% \right)\right),}}
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    DLMF:6.7.E3
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