DLMF:6.7.E4 (Q2257)

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DLMF:6.7.E4
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    Statements

    test
    ∫ x ∞ t ⁢ e i ⁢ t a 2 + t 2 ⁢ d t = 1 2 ⁢ ( e a ⁢ E 1 ⁡ ( a - i ⁢ x ) + e - a ⁢ E 1 ⁡ ( - a - i ⁢ x ) ) , superscript subscript 𝑥 𝑡 superscript 𝑒 𝑖 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 superscript 𝑒 𝑎 exponential-integral 𝑎 𝑖 𝑥 superscript 𝑒 𝑎 exponential-integral 𝑎 𝑖 𝑥 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{te^{it}}{a^{2}+t^{2}}% \mathrm{d}t=\tfrac{1}{2}\left(e^{a}E_{1}\left(a-ix\right)+e^{-a}E_{1}\left(-a-% ix\right)\right),}}
    0 references
    DLMF id
    DLMF:6.7.E4
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    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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