DLMF:8.6.E11 (Q2525)

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DLMF:8.6.E11
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    Statements

    test
    Γ ⁡ ( a , z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s + a ) ⁢ z - s s ⁢ d s , incomplete-Gamma 𝑎 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 𝑎 superscript 𝑧 𝑠 𝑠 𝑠 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{1}{2\pi i}\int_{c-i% \infty}^{c+i\infty}\Gamma\left(s+a\right)\frac{z^{-s}}{s}\mathrm{d}s,}}
    0 references
    DLMF id
    DLMF:8.6.E11
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
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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.m2addec
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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.m2aedec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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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
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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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
    0 references
    Q11331
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C8.S6.XMD1.m1adec
    0 references
     
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