  By applying multiplicate forms of the Carlitz inverse series relations to the
$q$-Pfaff-Saalsch{\"u}tz summation theorem, we establish twenty five
nonterminating $q$-series identities with several of them serving as
$q$-analogues of infinite series expressions for $\pi$ and $1/\pi$, including
some typical ones discovered by Ramanujan (1914) and Guillera.

Number Theory;Combinatorics