DLMF:6.7.E1 (Q2254): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 01:25, 2 January 2020

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DLMF:6.7.E1
No description defined

    Statements

    test
    ∫ 0 ∞ e - a ⁢ t t + b ⁢ d t = ∫ 0 ∞ e i ⁢ a ⁢ t t + i ⁢ b ⁢ d t = e a ⁢ b ⁢ E 1 ⁡ ( a ⁢ b ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 𝑡 𝑏 𝑡 superscript subscript 0 superscript 𝑒 𝑖 𝑎 𝑡 𝑡 𝑖 𝑏 𝑡 superscript 𝑒 𝑎 𝑏 exponential-integral 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{t+b}\mathrm{d}t=% \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\mathrm{d}t=e^{ab}E_{1}\left(ab\right),}}
    0 references
    DLMF id
    DLMF:6.7.E1
    0 references
    constraint
    b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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