DLMF:17.9.E13 (Q5439)

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Language	Label	Description	Also known as
English	DLMF:17.9.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop d,e};q,\frac{de}% {abc}\right)=\frac{\left(e/b,e/c;q\right)_{\infty}}{\left(e,e/(bc);q\right)_{% \infty}}{{}_{3}\phi_{2}}\left({d/a,b,c\atop d,bcq/e};q,q\right)+\frac{\left(d/% a,b,c,de/(bc);q\right)_{\infty}}{\left(d,e,bc/e,de/(abc);q\right)_{\infty}}{{}% _{3}\phi_{2}}\left({e/b,e/c,de/(abc)\atop de/(bc),eq/(bc)};q,q\right).}}

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DLMF:17.9.E13

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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.m2aldec

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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.m6aedec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1ldec

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