DLMF:10.22.E45 (Q3419): Difference between revisions

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Property / constraint
 

1 < μ < 3 1 𝜇 3 {\displaystyle{\displaystyle 1<\Re\mu<3}}

1<\realpart@@{\mu}<3
Property / constraint: 1 < μ < 3 1 𝜇 3 {\displaystyle{\displaystyle 1<\Re\mu<3}} / rank
 
Normal rank

Revision as of 16:20, 30 December 2019

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DLMF:10.22.E45
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    Statements

    0 1 - J 0 ( t ) t μ d t = - π sec ( 1 2 μ π ) 2 μ Γ 2 ( 1 2 μ + 1 2 ) , superscript subscript 0 1 Bessel-J 0 𝑡 superscript 𝑡 𝜇 𝑡 𝜋 1 2 𝜇 𝜋 superscript 2 𝜇 Euler-Gamma 2 1 2 𝜇 1 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{1-J_{0}\left(t\right)}{t^{% \mu}}\mathrm{d}t=-\frac{\pi\sec\left(\frac{1}{2}\mu\pi\right)}{2^{\mu}{\Gamma^% {2}}\left(\frac{1}{2}\mu+\frac{1}{2}\right)},}}
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    1 < μ < 3 1 𝜇 3 {\displaystyle{\displaystyle 1<\Re\mu<3}}
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