DLMF:18.27.E21 (Q5972)

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Language	Label	Description	Also known as
English	DLMF:18.27.E21	No description defined

Statements

Defining formula

{\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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Symbols defined

discrete $$q$$ -Hermite I polynomial

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Defining formula

{\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

introduction.Sx4.p1.t1.r17.m4adec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2agdec

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basic hypergeometric (or $$q$$ -hypergeometric) function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1sdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1pdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1odec

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