DLMF:5.9.E7 (Q2096)

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DLMF:5.9.E7
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    Statements

    test
    Γ ⁡ ( z ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ z ) = ∫ 0 ∞ t z - 1 ⁢ sin ⁡ t ⁢ d t , Euler-Gamma 𝑧 1 2 𝜋 𝑧 superscript subscript 0 superscript 𝑡 𝑧 1 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(z\right)\sin\left(\tfrac{1}{2}\pi z% \right)=\int_{0}^{\infty}t^{z-1}\sin t\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E7
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    constraint
    - 1 < ℜ ⁡ z < 1 1 𝑧 1 {\displaystyle{\displaystyle-1<\Re z<1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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