DLMF:18.33.E15 (Q6025)

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DLMF:18.33.E15
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    ϕ n ( z ) = = 0 n ( a q 2 ; q 2 ) ( a ; q 2 ) n - ( q 2 ; q 2 ) ( q 2 ; q 2 ) n - ( q - 1 z ) = ( a ; q 2 ) n ( q 2 ; q 2 ) n ϕ 1 2 ( a q 2 , q - 2 n a - 1 q 2 - 2 n ; q 2 , q z a ) , subscript italic-ϕ 𝑛 𝑧 superscript subscript 0 𝑛 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 superscript 𝑞 2 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 𝑛 q-Pochhammer-symbol superscript 𝑞 2 superscript 𝑞 2 q-Pochhammer-symbol superscript 𝑞 2 superscript 𝑞 2 𝑛 superscript superscript 𝑞 1 𝑧 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 𝑛 q-Pochhammer-symbol superscript 𝑞 2 superscript 𝑞 2 𝑛 q-hypergeometric-rphis 2 1 𝑎 superscript 𝑞 2 superscript 𝑞 2 𝑛 superscript 𝑎 1 superscript 𝑞 2 2 𝑛 superscript 𝑞 2 𝑞 𝑧 𝑎 {\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{\left(aq^{2};q^% {2}\right)_{\ell}\left(a;q^{2}\right)_{n-\ell}}{\left(q^{2};q^{2}\right)_{\ell% }\left(q^{2};q^{2}\right)_{n-\ell}}(q^{-1}z)^{\ell}=\frac{\left(a;q^{2}\right)% _{n}}{\left(q^{2};q^{2}\right)_{n}}{{}_{2}\phi_{1}}\left({aq^{2},q^{-2n}\atop a% ^{-1}q^{2-2n}};q^{2},\frac{qz}{a}\right),}}
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