DLMF:8.22.E1 (Q2750)

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DLMF:8.22.E1
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    Statements

    test
    F p ⁡ ( z ) = Γ ⁡ ( p ) 2 ⁢ π ⁢ z 1 - p ⁢ E p ⁡ ( z ) = Γ ⁡ ( p ) 2 ⁢ π ⁢ Γ ⁡ ( 1 - p , z ) , terminant-function 𝑝 𝑧 Euler-Gamma 𝑝 2 𝜋 superscript 𝑧 1 𝑝 exponential-integral-En 𝑝 𝑧 Euler-Gamma 𝑝 2 𝜋 incomplete-Gamma 1 𝑝 𝑧 {\displaystyle{\displaystyle F_{p}\left(z\right)=\frac{\Gamma\left(p\right)}{2% \pi}z^{1-p}E_{p}\left(z\right)=\frac{\Gamma\left(p\right)}{2\pi}\Gamma\left(1-% p,z\right),}}
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    DLMF id
    DLMF:8.22.E1
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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.m2adec
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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.m2adec
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    generalized exponential integral
    test
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.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.E2.m2adec
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    terminant function
    test
    F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C2.S11.E11.m2adec
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    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
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    Q11377
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1dec
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