DLMF:12.12.E1 (Q4226): Difference between revisions

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μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}

\realpart@@{\mu}>0
Property / constraint: μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}} / rank
 
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Revision as of 17:44, 30 December 2019

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DLMF:12.12.E1
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    0 e - 1 4 t 2 t μ - 1 U ( a , t ) d t = π 2 - 1 2 ( μ + a + 1 2 ) Γ ( μ ) Γ ( 1 2 ( μ + a + 3 2 ) ) , superscript subscript 0 superscript 𝑒 1 4 superscript 𝑡 2 superscript 𝑡 𝜇 1 parabolic-U 𝑎 𝑡 𝑡 𝜋 superscript 2 1 2 𝜇 𝑎 1 2 Euler-Gamma 𝜇 Euler-Gamma 1 2 𝜇 𝑎 3 2 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{1}{4}t^{2}}t^{\mu-1}U% \left(a,t\right)\mathrm{d}t=\frac{\sqrt{\pi}2^{-\frac{1}{2}(\mu+a+\frac{1}{2})% }\Gamma\left(\mu\right)}{\Gamma\left(\frac{1}{2}(\mu+a+\frac{3}{2})\right)},}}
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    DLMF:12.12.E1
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    μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
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