DLMF:10.22.E19 (Q3393): Difference between revisions

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Property / constraint
 

ℜ ⁡ ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}

\realpart@@{\nu}>-1
Property / constraint: ℜ ⁡ ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}} / rank
 
Normal rank

Revision as of 17:19, 30 December 2019

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DLMF:10.22.E19
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    Statements

    test
    ∫ 0 1 2 ⁢ π J μ ⁡ ( z ⁢ sin ⁡ θ ) ⁢ ( sin ⁡ θ ) μ + 1 ⁢ ( cos ⁡ θ ) 2 ⁢ ν + 1 ⁢ d θ = 2 ν ⁢ Γ ⁡ ( ν + 1 ) ⁢ z - ν - 1 ⁢ J μ + ν + 1 ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-J 𝜇 𝑧 𝜃 superscript 𝜃 𝜇 1 superscript 𝜃 2 𝜈 1 𝜃 superscript 2 𝜈 Euler-Gamma 𝜈 1 superscript 𝑧 𝜈 1 Bessel-J 𝜇 𝜈 1 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z\sin\theta% \right)(\sin\theta)^{\mu+1}(\cos\theta)^{2\nu+1}\mathrm{d}\theta=2^{\nu}\Gamma% \left(\nu+1\right)z^{-\nu-1}J_{\mu+\nu+1}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.22.E19
    0 references
    constraint
    ℜ ⁡ μ > - 1 𝜇 1 {\displaystyle{\displaystyle\Re\mu>-1}}
    0 references
    ℜ ⁡ ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
    0 references
     
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