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

$q$-Analogues of $\pi$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{\"u}tz Theorem