Formula:6680

Digital Library of Mathematical Functions ID 18.28.E9

${\displaystyle{\displaystyle Q_{n}\left(\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y});a,b\,|\,q^{-1}\right)=(-1)^{n}b^{n}q^{-\frac{1}{2}n(n-1)}\*\left((ab)^{-1};q\right)_{n}{{}_{3}\phi_{1}}\left({q^{-n},q^{-y},a^{-2}q^{y}\atop(ab)^{-1}};q,q^{n}ab^{-1}\right).}}$

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
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle q}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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