DLMF:8.21.E12 (Q2734)

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DLMF:8.21.E12
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    Statements

    Defining formula
    Si ⁡ ( a , ∞ ) = Γ ⁡ ( a ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ a ) , generalized-sine-integral-Si 𝑎 Euler-Gamma 𝑎 1 2 𝜋 𝑎 {\displaystyle{\displaystyle\mathrm{Si}\left(a,\infty\right)=\Gamma\left(a% \right)\sin\left(\tfrac{1}{2}\pi a\right),}}
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    DLMF id
    DLMF:8.21.E12
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    constraint
    a ≠ - 1 , - 3 , - 5 , … 𝑎 1 3 5 … {\displaystyle{\displaystyle a\neq-1,-3,-5,\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.m2acdec
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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.m2aedec
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    generalized sine integral
    Defining formula
    Si ⁡ ( a , z ) generalized-sine-integral-Si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m3addec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
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    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1idec
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