DLMF:17.9.E12

MaRDI QIDQ6135

• Label: DLMF:17.9.E12

Digital Library of Mathematical Functions ID 17.9.E12

${\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop d,e};q,\frac{de}{abc}\right)=\frac{\left(e/b,e/c,cq/a,q/d;q\right)_{\infty}}{\left(e,cq/d,q/a,e/(bc);q\right)_{\infty}}{{}_{3}\phi_{2}}\left({c,d/a,cq/e\atop cq/a,bcq/e};q,\frac{bq}{d}\right)-\frac{\left(q/d,eq/d,b,c,d/a,de/(bcq),bcq^{2}/(de);q\right)_{\infty}}{\left(d/q,e,bq/d,cq/d,q/a,e/(bc),bcq/e;q\right)_{\infty}}{{}_{3}\phi_{2}}\left({aq/d,bq/d,cq/d\atop q^{2}/d,eq/d};q,\frac{de}{abc}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$: basic hypergeometric (or $$q$$ -hypergeometric) function
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
 

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