DLMF:8.21.E1 (Q2722)

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DLMF:8.21.E1
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    Statements

    Defining formula
    ci ⁡ ( a , z ) ± i ⁢ si ⁡ ( a , z ) = e ± 1 2 ⁢ π ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ⁢ e ∓ 1 2 ⁢ π ⁢ i ) , plus-or-minus generalized-cosine-integral-ci 𝑎 𝑧 𝑖 generalized-sine-integral-si 𝑎 𝑧 superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 minus-or-plus 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\mathrm{ci}\left(a,z\right)\pm i\mathrm{si}\left(a% ,z\right)=e^{\pm\frac{1}{2}\pi ia}\Gamma\left(a,ze^{\mp\frac{1}{2}\pi i}\right% ),}}
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    DLMF id
    DLMF:8.21.E1
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