$q$-Analogues of $π$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{ü}tz Theorem
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.
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Number Theory
Combinatorics
33D15, 05A30, 11B65, 33D05