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DLMF:8.19.E10 - MaRDI portal

DLMF:8.19.E10 (Q3394)

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DLMF:8.19.E10
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    Statements

    DLMF defining formula
    E p ⁡ ( z ) = z p - 1 ⁢ Γ ⁡ ( 1 - p ) - ∑ k = 0 ∞ ( - z ) k k ! ⁢ ( 1 - p + k ) , exponential-integral-En 𝑝 𝑧 superscript 𝑧 𝑝 1 Euler-Gamma 1 𝑝 superscript subscript 𝑘 0 superscript 𝑧 𝑘 𝑘 1 𝑝 𝑘 {\displaystyle{\displaystyle E_{p}\left(z\right)=z^{p-1}\Gamma\left(1-p\right)% -\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(1-p+k)},}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    generalized exponential integral
    DLMF defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2andec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1hdec
    0 references
    parameter
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1fdec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1cdec
    0 references

    Identifiers

     
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