DLMF:8.2.E8 (Q2488)

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DLMF:8.2.E8
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    Statements

    test
    γ ⁡ ( a , z ⁢ e 2 ⁢ π ⁢ m ⁢ i ) = e 2 ⁢ π ⁢ m ⁢ i ⁢ a ⁢ γ ⁡ ( a , z ) , incomplete-gamma 𝑎 𝑧 superscript 𝑒 2 𝜋 𝑚 𝑖 superscript 𝑒 2 𝜋 𝑚 𝑖 𝑎 incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(a,ze^{2\pi mi}\right)=e^{2\pi mia}% \gamma\left(a,z\right),}}
    0 references
    DLMF id
    DLMF:8.2.E8
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    constraint
    a ≠ 0 , - 1 , - 2 , … 𝑎 0 1 2 … {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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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.E1.m2addec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1gdec
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    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1gdec
    0 references
    Q11327
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C8.S2.XMD1.m1dec
    0 references
     
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