DLMF:17.6.E8 (Q5375)

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Language	Label	Description	Also known as
English	DLMF:17.6.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(\ifrac{abz}{c};q\right)_{\infty}}{\left(z;q\right)_{\infty}}{{}_{2% }\phi_{1}}\left({c/a,c/b\atop c};q,\ifrac{abz}{c}\right),}}

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DLMF:17.6.E8

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{\displaystyle{\displaystyle|z|<1,|abz|<|c|}}

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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.m2agdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1gdec

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Defining formula

{\displaystyle{\displaystyle z}}

C17.S1.XMD7.m1bdec

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