DLMF:8.21.E2 (Q2723)

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DLMF:8.21.E2
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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.E2
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    incomplete gamma function
    Defining formula
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2adec
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