Formula:6050

Digital Library of Mathematical Functions ID 17.4.E4

${\displaystyle{\displaystyle\lim_{q\to 1-}{{}_{r}\psi_{r}}\left({q^{a_{1}},q^{a_{2}},\dots,q^{a_{r}}\atop q^{b_{1}},q^{b_{2}},\dots,q^{b_{r}}};q,z\right)={{}_{r}H_{r}}\left({a_{1},a_{2},\dots,a_{r}\atop b_{1},b_{2},\dots,b_{r}};z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}H_{\NVar{q}}}\left({\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}};\NVar{z}\right)}}$: bilateral hypergeometric function
• ${\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$: bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle r}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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