DLMF:17.6.E9

MaRDI QIDQ6073

• Label: DLMF:17.6.E9

Digital Library of Mathematical Functions ID 17.6.E9

${\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q,aq\atop bq};q,z\right)=-\frac{(1-b)(aq/b)}{(1-(\ifrac{aq}{b}))}\sum_{n=0}^{\infty}\frac{\left(aq,azq/b;q\right)_{n}q^{n}}{\left(azq^{2}/b;q\right)_{n}}+\frac{\left(aq,azq/b;q\right)_{\infty}}{\left(aq/b;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({q,0\atop bq};q,z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1}}$

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
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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