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DLMF:8.4.E4 - MaRDI portal

DLMF:8.4.E4 (Q3196)

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DLMF:8.4.E4
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    Statements

    DLMF defining formula
    Γ ⁡ ( 0 , z ) = ∫ z ∞ t - 1 ⁢ e - t ⁢ d t = E 1 ⁡ ( z ) , incomplete-Gamma 0 𝑧 superscript subscript 𝑧 superscript 𝑡 1 superscript 𝑒 𝑡 𝑡 exponential-integral 𝑧 {\displaystyle{\displaystyle\Gamma\left(0,z\right)=\int_{z}^{\infty}t^{-1}e^{-% t}\mathrm{d}t=E_{1}\left(z\right),}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    exponential integral
    DLMF defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    incomplete gamma function
    DLMF defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1bdec
    0 references

    Identifiers

     
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