Simple Series
Some simple series expressions include
![\frac{z}{1-q} \;_{2}\phi_1 \left[\begin{matrix}
q \; q \\
q^2 \end{matrix}\; ; q,z \right] =
\frac{z}{1-q}
+ \frac{z^2}{1-q^2}
+ \frac{z^3}{1-q^3}
+ \ldots](http://upload.wikimedia.org/math/7/e/8/7e8df00949af12cfad161caaacbe12f5.png)
and
![\frac{z}{1-q^{1/2}} \;_{2}\phi_1 \left[\begin{matrix}
q \; q^{1/2} \\
q^{3/2} \end{matrix}\; ; q,z \right] =
\frac{z}{1-q^{1/2}}
+ \frac{z^2}{1-q^{3/2}}
+ \frac{z^3}{1-q^{5/2}}
+ \ldots](http://upload.wikimedia.org/math/1/c/f/1cfa9f8cfcd4b2965a0594635e0d9e50.png)
and
![\;_{2}\phi_1 \left[\begin{matrix}
q \; -1 \\
-q \end{matrix}\; ; q,z \right] = 1+
\frac{2z}{1+q}
+ \frac{2z^2}{1+q^2}
+ \frac{2z^3}{1+q^3}
+ \ldots.](http://upload.wikimedia.org/math/5/2/3/523611058a40eedf1dd82fdae8c7ddc1.png)
Read more about this topic: Basic Hypergeometric Series
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