DLMF:18.27.E21 (Q5972)

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DLMF:18.27.E21
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    h n ( x ; q ) = ( q ; q ) n = 0 n / 2 ( - 1 ) q ( - 1 ) x n - 2 ( q 2 ; q 2 ) ( q ; q ) n - 2 = x n ϕ 0 2 ( q - n , q - n + 1 - ; q 2 , x - 2 q 2 n - 1 ) . discrete-q-Hermite-polynomial-h-I 𝑛 𝑥 𝑞 q-Pochhammer-symbol 𝑞 𝑞 𝑛 superscript subscript 0 𝑛 2 superscript 1 superscript 𝑞 1 superscript 𝑥 𝑛 2 q-Pochhammer-symbol superscript 𝑞 2 superscript 𝑞 2 q-Pochhammer-symbol 𝑞 𝑞 𝑛 2 superscript 𝑥 𝑛 q-hypergeometric-rphis 2 0 superscript 𝑞 𝑛 superscript 𝑞 𝑛 1 superscript 𝑞 2 superscript 𝑥 2 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle h_{n}\left(x;q\right)=\left(q;q\right)_{n}\sum_{% \ell=0}^{\left\lfloor n/2\right\rfloor}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2% \ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q;q\right)_{n-2\ell}}=x^{n}{{}_{2}% \phi_{0}}\left({q^{-n},q^{-n+1}\atop-};q^{2},x^{-2}q^{2n-1}\right).}}
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    DLMF:18.27.E21
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