DLMF:18.28.E17 (Q5992)

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DLMF:18.28.E17
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    1 2 π 0 π H n ( cos θ | q ) H m ( cos θ | q ) | ( e 2 i θ ; q ) | 2 d θ = δ n , m ( q n + 1 ; q ) . 1 2 𝜋 superscript subscript 0 𝜋 continuous-q-Hermite-polynomial-H 𝑛 𝜃 𝑞 continuous-q-Hermite-polynomial-H 𝑚 𝜃 𝑞 q-Pochhammer-symbol superscript 𝑒 2 imaginary-unit 𝜃 𝑞 2 𝜃 Kronecker 𝑛 𝑚 q-Pochhammer-symbol superscript 𝑞 𝑛 1 𝑞 {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{0}^{\pi}H_{n}\left(\cos\theta% \,|\,q\right)H_{m}\left(\cos\theta\,|\,q\right){\left|\left(e^{2\mathrm{i}% \theta};q\right)_{\infty}\right|^{2}}\mathrm{d}\theta=\frac{\delta_{n,m}}{% \left(q^{n+1};q\right)_{\infty}}.}}
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    DLMF:18.28.E17
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