DLMF:10.22.E17 (Q3391): Difference between revisions

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Property / constraint
 

- 1 2 < ℜ ⁡ ν < 1 2 1 2 𝜈 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}<\Re\nu<\tfrac{1}{2}}}

-\tfrac{1}{2}<\realpart@@{\nu}<\tfrac{1}{2}
Property / constraint: - 1 2 < ℜ ⁡ ν < 1 2 1 2 𝜈 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}<\Re\nu<\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 16:19, 30 December 2019

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DLMF:10.22.E17
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    Statements

    test
    ∫ 0 1 2 ⁢ π Y 2 ⁢ ν ⁡ ( 2 ⁢ z ⁢ cos ⁡ θ ) ⁢ cos ⁡ ( 2 ⁢ μ ⁢ θ ) ⁢ d θ = 1 2 ⁢ π ⁢ cot ⁡ ( 2 ⁢ ν ⁢ π ) ⁢ J ν + μ ⁡ ( z ) ⁢ J ν - μ ⁡ ( z ) - 1 2 ⁢ π ⁢ csc ⁡ ( 2 ⁢ ν ⁢ π ) ⁢ J μ - ν ⁡ ( z ) ⁢ J - μ - ν ⁡ ( z ) , superscript subscript 0 1 2 𝜋 Bessel-Y-Weber 2 𝜈 2 𝑧 𝜃 2 𝜇 𝜃 𝜃 1 2 𝜋 2 𝜈 𝜋 Bessel-J 𝜈 𝜇 𝑧 Bessel-J 𝜈 𝜇 𝑧 1 2 𝜋 2 𝜈 𝜋 Bessel-J 𝜇 𝜈 𝑧 Bessel-J 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}Y_{2\nu}\left(2z\cos% \theta\right)\cos\left(2\mu\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi\cot% \left(2\nu\pi\right)J_{\nu+\mu}\left(z\right)J_{\nu-\mu}\left(z\right)-\tfrac{% 1}{2}\pi\csc\left(2\nu\pi\right)J_{\mu-\nu}\left(z\right)J_{-\mu-\nu}\left(z% \right),}}
    0 references
    DLMF id
    DLMF:10.22.E17
    0 references
    constraint
    - 1 2 < ℜ ⁡ ν < 1 2 1 2 𝜈 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}<\Re\nu<\tfrac{1}{2}}}
    0 references
     
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