DLMF:10.22.E21 (Q3395): Difference between revisions

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Property / constraint
 

ℜ ⁡ μ > - 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}

\realpart@@{\mu}>-\tfrac{1}{2}
Property / constraint: ℜ ⁡ μ > - 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 16:19, 30 December 2019

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DLMF:10.22.E21
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    Statements

    test
    ∫ 0 1 2 ⁢ π Y μ ⁡ ( z ⁢ sin ⁡ θ ) ⁢ ( sin ⁡ θ ) μ ⁢ ( cos ⁡ θ ) 2 ⁢ μ ⁢ d θ = π 1 2 ⁢ 2 μ - 1 ⁢ z - μ ⁢ Γ ⁡ ( μ + 1 2 ) ⁢ J μ ⁡ ( 1 2 ⁢ z ) ⁢ Y μ ⁡ ( 1 2 ⁢ z ) , superscript subscript 0 1 2 𝜋 Bessel-Y-Weber 𝜇 𝑧 𝜃 superscript 𝜃 𝜇 superscript 𝜃 2 𝜇 𝜃 superscript 𝜋 1 2 superscript 2 𝜇 1 superscript 𝑧 𝜇 Euler-Gamma 𝜇 1 2 Bessel-J 𝜇 1 2 𝑧 Bessel-Y-Weber 𝜇 1 2 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}Y_{\mu}\left(z\sin\theta% \right)(\sin\theta)^{\mu}(\cos\theta)^{2\mu}\mathrm{d}\theta=\pi^{\frac{1}{2}}% 2^{\mu-1}z^{-\mu}\*\Gamma\left(\mu+\tfrac{1}{2}\right)J_{\mu}\left(\tfrac{1}{2% }z\right)Y_{\mu}\left(\tfrac{1}{2}z\right),}}
    0 references
    DLMF id
    DLMF:10.22.E21
    0 references
    constraint
    ℜ ⁡ μ > - 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}
    0 references
     
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