DLMF:17.9.E3

MaRDI QIDQ6126

• Label: DLMF:17.9.E3

Digital Library of Mathematical Functions ID 17.9.E3

${\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=\frac{\left(abz/c;q\right)_{\infty}}{\left(bz/c;q\right)_{\infty}}{{}_{3}\phi_{2}}\left({a,c/b,0\atop c,cq/(bz)};q,q\right)+\frac{\left(a,bz,c/b;q\right)_{\infty}}{\left(c,z,c/(bz);q\right)_{\infty}}{{}_{3}\phi_{2}}\left({z,abz/c,0\atop bz,bzq/c};q,q\right),}}$

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

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