DLMF:17.9.E14 (Q5440)

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Language	Label	Description	Also known as
English	DLMF:17.9.E14	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},a,b,c\atop d,e,f};q,% q\right)=\frac{\left(e/a,f/a;q\right)_{n}}{\left(e,f;q\right)_{n}}a^{n}{{}_{4}% \phi_{3}}\left({q^{-n},a,d/b,d/c\atop d,aq^{1-n}/e,aq^{1-n}/f};q,q\right)=% \frac{\left(a,ef/(ab),ef/(ac);q\right)_{n}}{\left(e,f,ef/(abc);q\right)_{n}}{{% }_{4}\phi_{3}}\left({q^{-n},e/a,f/a,ef/(abc)\atop ef/(ab),ef/(ac),q^{1-n}/a};q% ,q\right).}}

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DLMF:17.9.E14

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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.m2amdec

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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.m6afdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1mdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1gdec

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