DLMF:8.21.E3 (Q2724)

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DLMF:8.21.E3
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    Statements

    Defining formula
    ∫ 0 ∞ t a - 1 ⁢ e ± i ⁢ t ⁢ d t = e ± 1 2 ⁢ π ⁢ i ⁢ a ⁢ Γ ⁡ ( a ) , superscript subscript 0 superscript 𝑡 𝑎 1 superscript 𝑒 plus-or-minus imaginary-unit 𝑡 𝑡 superscript 𝑒 plus-or-minus 1 2 𝜋 imaginary-unit 𝑎 Euler-Gamma 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{a-1}e^{\pm\mathrm{i}t}\mathrm{% d}t=e^{\pm\frac{1}{2}\pi\mathrm{i}a}\Gamma\left(a\right),}}
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    DLMF id
    DLMF:8.21.E3
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        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2724&oldid=8724"