Q超幾何級数
.. , b r − 1 , q ; q ) n z n r ψ r [ a 1 , a 2 , ⋯ , a r b 1 , b 2 , ⋯ , b r ; q , z ] = ∑ n = − ∞ ∞ ( a 1 , a 2 , ... , a r ; q ) n ( b 1 , b 2 , ... , b r ; q ) n z n {\displaystyle {\begin{aligned}{}_{r}\phi _{r-1}\left[{\begin{matrix}a_{1},a_{2},\dotsc ,a_{r}\\b_{1},b_{2},\dotsc ,b_{r-1}\end{matrix}};q,z\right]&=\sum _{n=0}^{\infty }{\frac {(a_{1},a_{2},\dotsc ,a_{r};q)_{n}}{(b_{1},b_{2},\dotsc ,b_{r-1},q;q)_{n}}}z^{n}\\{}_{r}\psi _{r}\left[{\begin{matrix}a_{1},a_{2},\dotsb ,a_{r}\\b_{1},b_{2},\dotsb ,b_{r}\end{matrix}};q,z\right]&=\sum _{n=-\infty }^{\infty }{\frac {(a_{1},a_{2},\dotsc ,a_{r};q)_{n}}{(b_{1},b_{2},\dotsc ,b_{r};q)_{n}}}z^{n}\\\end{aligned}}}