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DLMF:33.16#Ex9 - MaRDI portal

DLMF:33.16#Ex9 (Q10341)

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DLMF:33.16#Ex9
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    DLMF defining formula
    s ⁡ ( ϵ , ℓ ; r ) = ( - 1 ) ℓ + 1 2 1 / 2 ⁢ ( ν 3 / 2 K ⁢ ( ν , ℓ ) ⁢ ξ ℓ ⁢ ( - ν , r ) - sin ⁡ ( π ⁢ ν ) ⁢ cos ⁡ ( π ⁢ ν ) π ⁢ ν 1 / 2 ⁢ K ⁢ ( ν , ℓ ) ⁢ ζ ℓ ⁢ ( - ν , r ) ) , Coulomb-s italic-ϵ ℓ 𝑟 superscript 1 ℓ 1 superscript 2 1 2 superscript 𝜈 3 2 𝐾 𝜈 ℓ subscript 𝜉 ℓ 𝜈 𝑟 𝜋 𝜈 𝜋 𝜈 𝜋 superscript 𝜈 1 2 𝐾 𝜈 ℓ subscript 𝜁 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle s\left(\epsilon,\ell;r\right)=\frac{(-1)^{\ell+1}% }{2^{1/2}}\left(\frac{\nu^{3/2}}{K(\nu,\ell)}\xi_{\ell}(-\nu,r)-\frac{\sin% \left(\pi\nu\right)\cos\left(\pi\nu\right)}{\pi\nu^{1/2}}K(\nu,\ell)\zeta_{% \ell}(-\nu,r)\right),}}
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