DLMF:18.27.E18 (Q5969)

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Language	Label	Description	Also known as
English	DLMF:18.27.E18	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle S_{n}\left(x;q\right)=\sum_{\ell=0}^{n}\frac{q^{% \ell^{2}}(-x)^{\ell}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}=\frac{% 1}{\left(q;q\right)_{n}}{{}_{1}\phi_{1}}\left({q^{-n}\atop 0};q,-q^{n+1}x% \right).}}

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DLMF:18.27.E18

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Symbols defined

Stieltjes–Wigert polynomial

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Defining formula

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

C17.S2.SS1.p1.m2addec

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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.m2addec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1pdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1mdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1ldec

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Sitelinks

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