DLMF:6.7.E8 (Q2261): Difference between revisions

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Property / constraint
 

a , b 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}}

a,b\in\Reals
Property / constraint: a , b 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}} / rank
 
Normal rank

Revision as of 17:06, 30 December 2019

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DLMF:6.7.E8
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    Statements

    0 1 e - a t ( 1 - cos ( b t ) ) t d t = Ein ( a + i b ) - Ein ( a ) , superscript subscript 0 1 superscript 𝑒 𝑎 𝑡 1 𝑏 𝑡 𝑡 𝑡 complementary-exponential-integral 𝑎 𝑖 𝑏 complementary-exponential-integral 𝑎 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at}(1-\cos\left(bt\right))}{% t}\mathrm{d}t=\Re\mathrm{Ein}\left(a+ib\right)-\mathrm{Ein}\left(a\right),}}
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    a , b 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}}
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