DLMF:8.19.E24 (Q2710)

From testwiki
Revision as of 16:12, 30 December 2019 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
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
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2710&oldid=13772"