DLMF:16.11.E6 (Q5240)

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DLMF:16.11.E6
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    ( ∏ ℓ = 1 q + 1 Γ ⁡ ( a ℓ ) / ∏ ℓ = 1 q Γ ⁡ ( b ℓ ) ) ⁢ F q q + 1 ⁡ ( a 1 , … , a q + 1 b 1 , … , b q ; z ) = H q + 1 , q ⁢ ( - z ) , superscript subscript product ℓ 1 𝑞 1 Euler-Gamma subscript 𝑎 ℓ superscript subscript product ℓ 1 𝑞 Euler-Gamma subscript 𝑏 ℓ Gauss-hypergeometric-pFq 𝑞 1 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑞 1 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 subscript 𝐻 𝑞 1 𝑞 𝑧 {\displaystyle{\displaystyle\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{q+1% }\Gamma\left(a_{\ell}\right)}{\prod\limits_{\ell=1}^{q}\Gamma\left(b_{\ell}% \right)}}\right){{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{1},\dots,b_{% q}};z\right)=H_{q+1,q}(-z),}}
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    DLMF:16.11.E6
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