DLMF:2.11.E5 (Q1030)

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DLMF:2.11.E5
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    Statements

    Defining formula
    E p ⁡ ( z ) = e - z ⁢ z p - 1 Γ ⁡ ( p ) ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t p - 1 1 + t ⁢ d t exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 superscript 𝑧 𝑝 1 Euler-Gamma 𝑝 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑝 1 1 𝑡 𝑡 {\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{e^{-z}z^{p-1}}{\Gamma% \left(p\right)}\int_{0}^{\infty}\frac{e^{-zt}t^{p-1}}{1+t}\mathrm{d}t}}
    0 references
    DLMF id
    DLMF:2.11.E5
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    generalized exponential integral
    Defining formula
    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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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
     
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