DLMF:17.6.E26 (Q5393)

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Language	Label	Description	Also known as
English	DLMF:17.6.E26	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}\left(\frac{\left(z;q\right)_{% \infty}}{\left(abz/c;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z% \right)\right)=\frac{\left(c/a,c/b;q\right)_{n}}{\left(c;q\right)_{n}(1-q)^{n}% }\left(\frac{ab}{c}\right)^{n}\frac{\left(zq^{n};q\right)_{\infty}}{\left(abz/% c;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({a,b\atop cq^{n}};q,zq^{n}\right).}}

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DLMF:17.6.E26

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Defining formula

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

C17.S2.SS1.p1.m2ajdec

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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.m2aydec

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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.m6andec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1ydec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1hdec

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Defining formula

{\displaystyle{\displaystyle z}}

C17.S1.XMD7.m1sdec

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$$q$$ -differential operator (locally)

Defining formula

{\displaystyle{\displaystyle\mathcal{D}_{q}}}

C17.S2.XMD1.m1adec

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