DLMF:12.12.E2 (Q4227): Difference between revisions

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Property / constraint
 

a < - 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<-\tfrac{1}{2}}}

\realpart@@{a}<-\tfrac{1}{2}
Property / constraint: a < - 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:44, 30 December 2019

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DLMF:12.12.E2
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    0 e - 3 4 t 2 t - a - 3 2 U ( a , t ) d t = 2 1 4 + 1 2 a Γ ( - a - 1 2 ) cos ( ( 1 4 a + 1 8 ) π ) , superscript subscript 0 superscript 𝑒 3 4 superscript 𝑡 2 superscript 𝑡 𝑎 3 2 parabolic-U 𝑎 𝑡 𝑡 superscript 2 1 4 1 2 𝑎 Euler-Gamma 𝑎 1 2 1 4 𝑎 1 8 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{3}{4}t^{2}}t^{-a-\frac{% 3}{2}}U\left(a,t\right)\mathrm{d}t=2^{\frac{1}{4}+\frac{1}{2}a}\Gamma\left(-a-% \tfrac{1}{2}\right)\cos\left((\tfrac{1}{4}a+\tfrac{1}{8})\pi\right),}}
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    DLMF:12.12.E2
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    a < - 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<-\tfrac{1}{2}}}
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