DLMF:7.14.E7 (Q2439): 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 16:09, 30 December 2019

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DLMF:7.14.E7
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    0 e - a t C ( 2 t π ) d t = ( a 2 + 1 + a ) 1 2 2 a a 2 + 1 , superscript subscript 0 superscript 𝑒 𝑎 𝑡 Fresnel-cosine-integral 2 𝑡 𝜋 𝑡 superscript superscript 𝑎 2 1 𝑎 1 2 2 𝑎 superscript 𝑎 2 1 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}C\left(\sqrt{\frac{2t}{\pi% }}\right)\mathrm{d}t=\frac{(\sqrt{a^{2}+1}+a)^{\frac{1}{2}}}{2a\sqrt{a^{2}+1}}% ,}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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