DLMF:17.9.E17

MaRDI QIDQ6140

• Label: DLMF:17.9.E17

Digital Library of Mathematical Functions ID 17.9.E17

${\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop aq/b,aq/c};q,\frac{aqz}{bc}\right)=\frac{\left(az;q\right)_{\infty}}{\left(z;q\right)_{\infty}}\*{{}_{5}\phi_{4}}\left({a^{\frac{1}{2}},-a^{\frac{1}{2}},(aq)^{\frac{1}{2}},-(aq)^{\frac{1}{2}},aq/(bc)\atop aq/b,aq/c,az,q/z};q,q\right).}}$

Symbols List

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

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