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DLMF:33.16#Ex8 - MaRDI portal

DLMF:33.16#Ex8 (Q10340)

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DLMF:33.16#Ex8
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    DLMF defining formula
    c ⁡ ( ϵ , ℓ ; r ) = ( - 1 ) ℓ 2 ⁢ ν 1 / 2 ⁢ ( cos ⁡ ( π ⁢ ν ) π ⁢ K ⁢ ( ν , ℓ ) ⁢ ξ ℓ ⁢ ( ν , r ) + sin ⁡ ( π ⁢ ν ) ⁢ ν 2 ⁢ K ⁢ ( ν , ℓ ) ⁢ ζ ℓ ⁢ ( ν , r ) ) . Coulomb-c italic-ϵ ℓ 𝑟 superscript 1 ℓ 2 superscript 𝜈 1 2 𝜋 𝜈 𝜋 𝐾 𝜈 ℓ subscript 𝜉 ℓ 𝜈 𝑟 𝜋 𝜈 superscript 𝜈 2 𝐾 𝜈 ℓ subscript 𝜁 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle c\left(\epsilon,\ell;r\right)=\frac{(-1)^{\ell}}{% 2\nu^{1/2}}\left(\frac{\cos\left(\pi\nu\right)}{\pi K(\nu,\ell)}\xi_{\ell}(\nu% ,r)+\sin\left(\pi\nu\right)\nu^{2}K(\nu,\ell)\zeta_{\ell}(\nu,r)\right).}}
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