DLMF:17.6.E7

MaRDI QIDQ6071

• Label: DLMF:17.6.E7

Digital Library of Mathematical Functions ID 17.6.E7

${\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=\frac{\left(c/b,bz;q\right)_{\infty}}{\left(c,z;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({\ifrac{abz}{c},b\atop bz};q,c/b\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1,|c|<|b|}}$

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
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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