DLMF:6.7.E6 (Q2259): Difference between revisions

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imported>Admin
Property / constraint
 

x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}

x\in\Reals
Property / constraint: x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}} / rank
 
Normal rank

Revision as of 17:06, 30 December 2019

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DLMF:6.7.E6
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    Statements

    x t e - t a 2 + t 2 d t = 1 2 ( e i a E 1 ( x + i a ) + e - i a E 1 ( x - i a ) ) , superscript subscript 𝑥 𝑡 superscript 𝑒 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}% \mathrm{d}t=\tfrac{1}{2}\left(e^{ia}E_{1}\left(x+ia\right)+e^{-ia}E_{1}\left(x% -ia\right)\right),}}
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    x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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