DLMF:18.27.E22 (Q5973)

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Language	Label	Description	Also known as
English	DLMF:18.27.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{\ell=0}^{\infty}\left(h_{n}\left(q^{\ell};q% \right)h_{m}\left(q^{\ell};q\right)+h_{n}\left(-q^{\ell};q\right)h_{m}\left(-q% ^{\ell};q\right)\right)\*\left(q^{\ell+1},-q^{\ell+1};q\right)_{\infty}q^{\ell% }=\left(q;q\right)_{n}\left({q,-1,-q};q\right)_{\infty}q^{n(n-1)/2}\delta_{n,m% }.}}

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DLMF:18.27.E22

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Defining formula

{\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

introduction.Sx4.p1.t1.r4.m5agdec

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discrete $$q$$ -Hermite I polynomial

Defining formula

{\displaystyle{\displaystyle h_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}

C18.S27.E21.m2aadec

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Defining formula

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

C17.S2.SS1.p1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6abdec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1tdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1gdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1qdec

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