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

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Property / constraint
 

b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}

b>0
Property / constraint: b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}} / rank
 
Normal rank

Revision as of 17:06, 30 December 2019

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DLMF:6.7.E1
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    Statements

    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),}}
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    b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}
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