DLMF:7.7.E5 (Q2375): Difference between revisions

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Property / constraint
 

a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}

\realpart@@{a}>0
Property / constraint: a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}} / rank
 
Normal rank

Revision as of 16:07, 30 December 2019

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DLMF:7.7.E5
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    0 1 e - a t 2 t 2 + 1 d t = π 4 e a ( 1 - ( erf a ) 2 ) , superscript subscript 0 1 superscript 𝑒 𝑎 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 𝜋 4 superscript 𝑒 𝑎 1 superscript error-function 𝑎 2 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at^{2}}}{t^{2}+1}\mathrm{d}t% =\frac{\pi}{4}e^{a}\left(1-(\operatorname{erf}\sqrt{a})^{2}\right),}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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