DLMF:8.2.E11 (Q2491)

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DLMF:8.2.E11
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    Statements

    test
    Γ ⁡ ( a , z ⁢ e ± π ⁢ i ) = Γ ⁡ ( a ) ⁢ ( 1 - z a ⁢ e ± π ⁢ i ⁢ a ⁢ γ * ⁡ ( a , - z ) ) . incomplete-Gamma 𝑎 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 Euler-Gamma 𝑎 1 superscript 𝑧 𝑎 superscript 𝑒 plus-or-minus 𝜋 𝑖 𝑎 incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(a,ze^{\pm\pi i}\right)=\Gamma\left(a% \right)(1-z^{a}e^{\pm\pi ia}\gamma^{*}\left(a,-z\right)).}}
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    DLMF id
    DLMF:8.2.E11
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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.m2acdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2aedec
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    incomplete gamma function
    test
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2abdec
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    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1jdec
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    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1jdec
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