DLMF:8.19.E11 (Q2697)

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DLMF:8.19.E11
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    Statements

    test
    E p ⁡ ( z ) = Γ ⁡ ( 1 - p ) ⁢ ( z p - 1 - e - z ⁢ ∑ k = 0 ∞ z k Γ ⁡ ( 2 - p + k ) ) , exponential-integral-En 𝑝 𝑧 Euler-Gamma 1 𝑝 superscript 𝑧 𝑝 1 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Euler-Gamma 2 𝑝 𝑘 {\displaystyle{\displaystyle E_{p}\left(z\right)=\Gamma\left(1-p\right)\left(z% ^{p-1}-e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Gamma\left(2-p+k\right)}\right),}}
    0 references
    DLMF id
    DLMF:8.19.E11
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.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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    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.m2aodec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1idec
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    Q11377
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1gdec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1ddec
    0 references
     
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