DLMF:18.33.E13 (Q6021)

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DLMF:18.33.E13
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    ϕ n ( z ) = = 0 n ( λ + 1 ) ( λ ) n - ! ( n - ) ! z = ( λ ) n n ! F 1 2 ( - n , λ + 1 - λ - n + 1 ; z ) , subscript italic-ϕ 𝑛 𝑧 superscript subscript 0 𝑛 Pochhammer 𝜆 1 Pochhammer 𝜆 𝑛 𝑛 superscript 𝑧 Pochhammer 𝜆 𝑛 𝑛 Gauss-hypergeometric-F-as-2F1 𝑛 𝜆 1 𝜆 𝑛 1 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{{\left(\lambda+% 1\right)_{\ell}}{\left(\lambda\right)_{n-\ell}}}{\ell!\,(n-\ell)!}\,z^{\ell}=% \frac{{\left(\lambda\right)_{n}}}{n!}{{}_{2}F_{1}}\left({-n,\lambda+1\atop-% \lambda-n+1};z\right),}}
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