DLMF:9.11.E15 (Q2922): Difference between revisions

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Property / constraint
 

α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}

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

Revision as of 17:14, 30 December 2019

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DLMF:9.11.E15
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    0 t α - 1 Ai 2 ( t ) d t = 2 Γ ( α ) π 1 / 2 12 ( 2 α + 5 ) / 6 Γ ( 1 3 α + 5 6 ) , superscript subscript 0 superscript 𝑡 𝛼 1 Airy-Ai 2 𝑡 𝑡 2 Euler-Gamma 𝛼 superscript 𝜋 1 2 superscript 12 2 𝛼 5 6 Euler-Gamma 1 3 𝛼 5 6 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}{\mathrm{Ai}^{2}}% \left(t\right)\mathrm{d}t=\frac{2\Gamma\left(\alpha\right)}{\pi^{1/2}12^{(2% \alpha+5)/6}\Gamma\left(\frac{1}{3}\alpha+\frac{5}{6}\right)},}}
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    α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}
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