DLMF:10.22.E23 (Q3397): Difference between revisions

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Property / constraint
 

ℜ ⁡ ( μ + α ) > 0 𝜇 𝛼 0 {\displaystyle{\displaystyle\Re(\mu+\alpha)>0}}

\realpart@@{(\mu+\alpha)}>0
Property / constraint: ℜ ⁡ ( μ + α ) > 0 𝜇 𝛼 0 {\displaystyle{\displaystyle\Re(\mu+\alpha)>0}} / rank
 
Normal rank

Revision as of 17:19, 30 December 2019

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DLMF:10.22.E23
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    Statements

    test
    ∫ 0 1 2 ⁢ π J μ ⁡ ( z ⁢ sin 2 ⁡ θ ) ⁢ J ν ⁡ ( z ⁢ cos 2 ⁡ θ ) ⁢ ( sin ⁡ θ ) 2 ⁢ α - 1 ⁢ sec ⁡ θ ⁢ d θ = ( μ + ν + α ) ⁢ Γ ⁡ ( μ + α ) ⁢ 2 α - 1 ν ⁢ Γ ⁡ ( μ + 1 ) ⁢ z α ⁢ J μ + ν + α ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-J 𝜇 𝑧 2 𝜃 Bessel-J 𝜈 𝑧 2 𝜃 superscript 𝜃 2 𝛼 1 𝜃 𝜃 𝜇 𝜈 𝛼 Euler-Gamma 𝜇 𝛼 superscript 2 𝛼 1 𝜈 Euler-Gamma 𝜇 1 superscript 𝑧 𝛼 Bessel-J 𝜇 𝜈 𝛼 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z{\sin^{2}}% \theta\right)J_{\nu}\left(z{\cos^{2}}\theta\right)(\sin\theta)^{2\alpha-1}\sec% \theta\mathrm{d}\theta=\frac{(\mu+\nu+\alpha)\Gamma\left(\mu+\alpha\right)2^{% \alpha-1}}{\nu\Gamma\left(\mu+1\right)z^{\alpha}}J_{\mu+\nu+\alpha}\left(z% \right),}}
    0 references
    DLMF id
    DLMF:10.22.E23
    0 references
    constraint
    ℜ ⁡ ( μ + α ) > 0 𝜇 𝛼 0 {\displaystyle{\displaystyle\Re(\mu+\alpha)>0}}
    0 references
     
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