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Formula:10261

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Digital Library of Mathematical Functions ID 33.10#Ex11

F ℓ ⁡ ( η , ρ ) = ( 2 ⁢ ℓ + 1 ) ! ⁢ C ℓ ⁡ ( η ) ( - 2 ⁢ η ) ℓ + 1 ⁢ ( ( - 2 ⁢ η ⁢ ρ ) 1 / 2 ⁢ J 2 ⁢ ℓ + 1 ⁡ ( ( - 8 ⁢ η ⁢ ρ ) 1 / 2 ) + o ⁡ ( | η | 1 / 4 ) ) , regular-Coulomb-F ℓ 𝜂 𝜌 2 ℓ 1 Coulomb-C ℓ 𝜂 superscript 2 𝜂 ℓ 1 superscript 2 𝜂 𝜌 1 2 Bessel-J 2 ℓ 1 superscript 8 𝜂 𝜌 1 2 little-o 𝜂 1 4 {\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=\dfrac{(2\ell+1)!C% _{\ell}\left(\eta\right)}{(-2\eta)^{\ell+1}}\left((-2\eta\rho)^{\ifrac{1}{2}}% \*J_{2\ell+1}\left((-8\eta\rho)^{\ifrac{1}{2}}\right)+o\left({\left|\eta\right% |^{\ifrac{1}{4}}}\right)\right),}}


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