DLMF:11.9.E5 (Q4012): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Lommel function / rank
 
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Revision as of 16:15, 30 December 2019

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DLMF:11.9.E5
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    Defining formula
    S μ , ν ⁡ ( z ) = s μ , ν ⁡ ( z ) + 2 μ - 1 ⁢ Γ ⁡ ( 1 2 ⁢ μ + 1 2 ⁢ ν + 1 2 ) ⁢ Γ ⁡ ( 1 2 ⁢ μ - 1 2 ⁢ ν + 1 2 ) ⁢ ( sin ⁡ ( 1 2 ⁢ ( μ - ν ) ⁢ π ) ⁢ J ν ⁡ ( z ) - cos ⁡ ( 1 2 ⁢ ( μ - ν ) ⁢ π ) ⁢ Y ν ⁡ ( z ) ) , Lommel-S 𝜇 𝜈 𝑧 Lommel-s 𝜇 𝜈 𝑧 superscript 2 𝜇 1 Euler-Gamma 1 2 𝜇 1 2 𝜈 1 2 Euler-Gamma 1 2 𝜇 1 2 𝜈 1 2 1 2 𝜇 𝜈 𝜋 Bessel-J 𝜈 𝑧 1 2 𝜇 𝜈 𝜋 Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)=s_{{\mu},{\nu}}% \left(z\right)+2^{\mu-1}\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{% 2}\right)\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\*% \left(\sin\left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,J_{\nu}\left(z\right)-\cos% \left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,Y_{\nu}\left(z\right)\right),}}
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    DLMF id
    DLMF:11.9.E5
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