DLMF:18.28.E16 (Q5991): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: continuous $$q$$ -Hermite polynomial / rank
 
Normal rank

Revision as of 16:22, 30 December 2019

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DLMF:18.28.E16
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    H n ( cos θ | q ) = = 0 n ( q ; q ) n e i ( n - 2 ) θ ( q ; q ) ( q ; q ) n - = e i n θ ϕ 0 2 ( q - n , 0 - ; q , q n e - 2 i θ ) . continuous-q-Hermite-polynomial-H 𝑛 𝜃 𝑞 superscript subscript 0 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 superscript 𝑒 imaginary-unit 𝑛 2 𝜃 q-Pochhammer-symbol 𝑞 𝑞 q-Pochhammer-symbol 𝑞 𝑞 𝑛 superscript 𝑒 imaginary-unit 𝑛 𝜃 q-hypergeometric-rphis 2 0 superscript 𝑞 𝑛 0 𝑞 superscript 𝑞 𝑛 superscript 𝑒 2 imaginary-unit 𝜃 {\displaystyle{\displaystyle H_{n}\left(\cos\theta\,|\,q\right)=\sum_{\ell=0}^% {n}\frac{\left(q;q\right)_{n}e^{\mathrm{i}(n-2\ell)\theta}}{\left(q;q\right)_{% \ell}\left(q;q\right)_{n-\ell}}=e^{\mathrm{i}n\theta}{{}_{2}\phi_{0}}\left({q^% {-n},0\atop-};q,q^{n}e^{-2\mathrm{i}\theta}\right).}}
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    DLMF:18.28.E16
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