DLMF:17.7.E8

MaRDI QIDQ6101

• Label: DLMF:17.7.E8

Digital Library of Mathematical Functions ID 17.7.E8

${\displaystyle{\displaystyle{{}_{8}\phi_{7}}\left({\lambda,q\lambda^{\frac{1}{2}},-q\lambda^{\frac{1}{2}},a,b,c,-c,\lambda q/c^{2}\atop\lambda^{\frac{1}{2}},-\lambda^{\frac{1}{2}},\lambda q/a,\lambda q/b,\lambda q/c,-\lambda q/c,c^{2}};q,-\frac{\lambda q}{ab}\right)=\frac{\left(\lambda q,c^{2}/\lambda;q\right)_{\infty}\left(aq,bq,c^{2}q/a,c^{2}q/b;q^{2}\right)_{\infty}}{\left(\lambda q/a,\lambda q/b;q\right)_{\infty}\left(q,abq,c^{2}q,c^{2}q/(ab);q^{2}\right)_{\infty}},}}$

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
 

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