DLMF:17.4.E3 (Q5352)

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Language	Label	Description	Also known as
English	DLMF:17.4.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{r}\psi_{s}}\left({a_{1},a_{2},\dots,a_{r}% \atop b_{1},b_{2},\dots,b_{s}};q,z\right)={{}_{r}\psi_{s}}\left(a_{1},a_{2},% \dots,a_{r};b_{1},b_{2},\dots,b_{s};q,z\right)=\sum_{n=-\infty}^{\infty}\frac{% \left(a_{1},a_{2},\dots,a_{r};q\right)_{n}(-1)^{(s-r)n}q^{(s-r)\genfrac{(}{)}{% 0.0pt}{}{n}{2}}z^{n}}{\left(b_{1},b_{2},\dots,b_{s};q\right)_{n}}=\sum_{n=0}^{% \infty}\frac{\left(a_{1},a_{2},\dots,a_{r};q\right)_{n}(-1)^{(s-r)n}q^{(s-r)% \genfrac{(}{)}{0.0pt}{}{n}{2}}z^{n}}{\left(b_{1},b_{2},\dots,b_{s};q\right)_{n% }}+\sum_{n=1}^{\infty}\frac{\left(q/b_{1},q/b_{2},\dots,q/b_{s};q\right)_{n}}{% \left(q/a_{1},q/a_{2},\dots,q/a_{r};q\right)_{n}}\left(\frac{b_{1}b_{2}\cdots b% _{s}}{a_{1}a_{2}\cdots a_{r}z}\right)^{n}.}}

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DLMF:17.4.E3

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Symbols defined

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

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1aadec

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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.m6adec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1bdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1adec

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Defining formula

{\displaystyle{\displaystyle r}}

C17.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle s}}

C17.S1.XMD6.m1adec

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Sitelinks

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