DLMF:8.21.E9 (Q2730)

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DLMF:8.21.E9
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    Statements

    Defining formula
    Ci ⁡ ( a , z ) = Γ ⁡ ( a ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ a ) - ci ⁡ ( a , z ) , generalized-cosine-integral-Ci 𝑎 𝑧 Euler-Gamma 𝑎 1 2 𝜋 𝑎 generalized-cosine-integral-ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,z\right)=\Gamma\left(a\right)% \cos\left(\tfrac{1}{2}\pi a\right)-\mathrm{ci}\left(a,z\right),}}
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    DLMF id
    DLMF:8.21.E9
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    constraint
    a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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