DLMF:33.16.E10 (Q9638)

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DLMF:33.16.E10
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    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) = ( - 1 ) ℓ ⁢ ν ℓ + 1 ⁢ ( - cos ⁡ ( π ⁢ ν ) ⁢ ζ ℓ ⁢ ( ν , r ) Γ ⁡ ( ℓ + 1 + ν ) + sin ⁡ ( π ⁢ ν ) ⁢ Γ ⁡ ( ν - ℓ ) ⁢ ξ ℓ ⁢ ( ν , r ) π ) , Coulomb-f italic-ϵ ℓ 𝑟 superscript 1 ℓ superscript 𝜈 ℓ 1 𝜋 𝜈 subscript 𝜁 ℓ 𝜈 𝑟 Euler-Gamma ℓ 1 𝜈 𝜋 𝜈 Euler-Gamma 𝜈 ℓ subscript 𝜉 ℓ 𝜈 𝑟 𝜋 {\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=(-1)^{\ell}\nu^{% \ell+1}\left(-\frac{\cos\left(\pi\nu\right)\zeta_{\ell}(\nu,r)}{\Gamma\left(% \ell+1+\nu\right)}+\frac{\sin\left(\pi\nu\right)\Gamma\left(\nu-\ell\right)\xi% _{\ell}(\nu,r)}{\pi}\right),}}
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    DLMF id
    DLMF:33.16.E10
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