DLMF:8.19.E7 (Q2693)

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DLMF:8.19.E7
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    Statements

    test
    E n ⁡ ( z ) = ( - z ) n - 1 ( n - 1 ) ! ⁢ E 1 ⁡ ( z ) + e - z ( n - 1 ) ! ⁢ ∑ k = 0 n - 2 ( n - k - 2 ) ! ⁢ ( - z ) k , exponential-integral-En 𝑛 𝑧 superscript 𝑧 𝑛 1 𝑛 1 exponential-integral 𝑧 superscript 𝑒 𝑧 𝑛 1 superscript subscript 𝑘 0 𝑛 2 𝑛 𝑘 2 superscript 𝑧 𝑘 {\displaystyle{\displaystyle E_{n}\left(z\right)=\frac{(-z)^{n-1}}{(n-1)!}E_{1% }\left(z\right)+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k},}}
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    DLMF id
    DLMF:8.19.E7
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    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
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    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
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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.m2akdec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1edec
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    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1dec
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    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1dec
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