DLMF:8.19.E24 (Q2710): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aedec

Revision as of 13:12, 2 January 2020

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DLMF:8.19.E24
No description defined

    Statements

    test
    ∫ 0 ∞ e - a ⁢ t ⁢ E n ⁡ ( t ) ⁢ d t = ( - 1 ) n - 1 a n ⁢ ( ln ⁡ ( 1 + a ) + ∑ k = 1 n - 1 ( - 1 ) k ⁢ a k k ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 exponential-integral-En 𝑛 𝑡 𝑡 superscript 1 𝑛 1 superscript 𝑎 𝑛 1 𝑎 superscript subscript 𝑘 1 𝑛 1 superscript 1 𝑘 superscript 𝑎 𝑘 𝑘 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}E_{n}\left(t\right)\mathrm% {d}t=\frac{(-1)^{n-1}}{a^{n}}\left(\ln\left(1+a\right)+\sum_{k=1}^{n-1}\frac{(% -1)^{k}a^{k}}{k}\right),}}
    0 references
    DLMF id
    DLMF:8.19.E24
    0 references
    constraint
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
    0 references
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
    0 references
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
     
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