DLMF:33.9.E4 (Q9554)

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DLMF:33.9.E4
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    Statements

    Defining formula
    F ℓ ⁡ ( η , ρ ) = C ℓ ⁡ ( η ) ⁢ ( 2 ⁢ ℓ + 1 ) ! ( 2 ⁢ | η | ) 2 ⁢ ℓ + 1 ⁢ ρ - ℓ ⁢ ∑ k = 2 ⁢ ℓ + 1 ∞ b k ⁢ t k / 2 ⁢ J k ⁡ ( 2 ⁢ t ) , regular-Coulomb-F ℓ 𝜂 𝜌 Coulomb-C ℓ 𝜂 2 ℓ 1 superscript 2 𝜂 2 ℓ 1 superscript 𝜌 ℓ superscript subscript 𝑘 2 ℓ 1 subscript 𝑏 𝑘 superscript 𝑡 𝑘 2 Bessel-J 𝑘 2 𝑡 {\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=C_{\ell}\left(\eta% \right)\frac{(2\ell+1)!}{(2\left|\eta\right|)^{2\ell+1}}\rho^{-\ell}\*\sum_{k=% 2\ell+1}^{\infty}\!\!b_{k}t^{k/2}J_{k}\left(\textstyle 2\sqrt{t}\right),}}
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    DLMF id
    DLMF:33.9.E4
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    constraint
    η < 0 𝜂 0 {\displaystyle{\displaystyle\eta<0}}
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