Formula:6091

Digital Library of Mathematical Functions ID 17.6.E27

${\displaystyle{\displaystyle z(c-abqz)\mathcal{D}_{q}^{2}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)+\left(\frac{1-c}{1-q}+\frac{(1-a)(1-b)-(1-abq)}{1-q}z\right)\mathcal{D}_{q}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)-\frac{(1-a)(1-b)}{(1-q)^{2}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=0.}}$

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
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\mathcal{D}_{q}}}$: $$q$$ -differential operator (locally)
 

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