Gold 91

Continuous q-Hermite polynomials

Gold ID

91

Link

https://sigir21.wmflabs.org/wiki/Continuous_q-Hermite_polynomials#math.150.3

Formula

$\sum _{n=0}^{\infty }H_{n}(x\mid q){\frac {t^{n}}{(q;q)_{n}}}={\frac {1}{\left(te^{i\theta },te^{-i\theta };q\right)_{\infty }}}$

TeX Source

\sum_{n=0}^\infty H_n(x \mid q) \frac{t^n}{(q;q)_n} = \frac{1}{\left( t e^{i \theta},t e^{-i \theta};q \right)_\infty}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Semantic LaTeX

Translation

\sum_{n=0}^\infty \HermitepolyH{n}@{x \mid q} \frac{t^n}{(q;q)_n} = \frac{1}{(t \expe^{\iunit \theta} , t \expe^{- \iunit \theta} ; q)_\infty}

Expected (Gold Entry)

\sum_{n=0}^\infty \contqHermitepolyH{n}@{x}{q} \frac{t^n}{\qmultiPochhammersym{q}{q}{n}} = \frac{1}{\qmultiPochhammersym{t \expe^{\iunit \theta} , t \expe^{- \iunit \theta}}{q}{\infty}}

Mathematica

Translation

Expected (Gold Entry)

Maple

Translation

Expected (Gold Entry)