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Formula:10262

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Digital Library of Mathematical Functions ID 33.10#Ex12

G ℓ ⁡ ( η , ρ ) = - π ⁢ ( - 2 ⁢ η ) ℓ ( 2 ⁢ ℓ + 1 ) ! ⁢ C ℓ ⁡ ( η ) ⁢ ( ( - 2 ⁢ η ⁢ ρ ) 1 / 2 ⁢ Y 2 ⁢ ℓ + 1 ⁡ ( ( - 8 ⁢ η ⁢ ρ ) 1 / 2 ) + o ⁡ ( | η | 1 / 4 ) ) . irregular-Coulomb-G ℓ 𝜂 𝜌 𝜋 superscript 2 𝜂 ℓ 2 ℓ 1 Coulomb-C ℓ 𝜂 superscript 2 𝜂 𝜌 1 2 Bessel-Y-Weber 2 ℓ 1 superscript 8 𝜂 𝜌 1 2 little-o 𝜂 1 4 {\displaystyle{\displaystyle G_{\ell}\left(\eta,\rho\right)=-\dfrac{\pi(-2\eta% )^{\ell}}{(2\ell+1)!C_{\ell}\left(\eta\right)}\left((-2\eta\rho)^{\ifrac{1}{2}% }\*Y_{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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