DLMF:33.6.E4 (Q9536)

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DLMF:33.6.E4
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    Defining formula
    A k ℓ ⁢ ( η ) = ( - i ) k - ℓ - 1 ( k - ℓ - 1 ) ! ⁢ F 1 2 ⁡ ( ℓ + 1 - k , ℓ + 1 - i ⁢ η ; 2 ⁢ ℓ + 2 ; 2 ) . superscript subscript 𝐴 𝑘 ℓ 𝜂 superscript imaginary-unit 𝑘 ℓ 1 𝑘 ℓ 1 Gauss-hypergeometric-F-as-2F1 ℓ 1 𝑘 ℓ 1 imaginary-unit 𝜂 2 ℓ 2 2 {\displaystyle{\displaystyle A_{k}^{\ell}(\eta)=\dfrac{(-\mathrm{i})^{k-\ell-1% }}{(k-\ell-1)!}\*{{}_{2}F_{1}}\left(\ell+1-k,\ell+1-\mathrm{i}\eta;2\ell+2;2% \right).}}
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    DLMF id
    DLMF:33.6.E4
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