DLMF:8.20.E1 (Q2714)

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DLMF:8.20.E1
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    Statements

    Defining formula
    E p ⁡ ( z ) = e - z z ⁢ ( ∑ k = 0 n - 1 ( - 1 ) k ⁢ ( p ) k z k + ( - 1 ) n ⁢ ( p ) n ⁢ e z z n - 1 ⁢ E n + p ⁡ ( z ) ) , exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑘 0 𝑛 1 superscript 1 𝑘 Pochhammer 𝑝 𝑘 superscript 𝑧 𝑘 superscript 1 𝑛 Pochhammer 𝑝 𝑛 superscript 𝑒 𝑧 superscript 𝑧 𝑛 1 exponential-integral-En 𝑛 𝑝 𝑧 {\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{e^{-z}}{z}\left(\sum_{k% =0}^{n-1}(-1)^{k}\frac{{\left(p\right)_{k}}}{z^{k}}+(-1)^{n}\frac{{\left(p% \right)_{n}}e^{z}}{z^{n-1}}E_{n+p}\left(z\right)\right),}}
    0 references
    DLMF id
    DLMF:8.20.E1
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    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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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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    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1dec
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    Q11377
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1dec
    0 references
    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1dec
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