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$q$-Analogues of $π$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{ü}tz Theorem (2102.12440v1)
Published 24 Feb 2021 in math.NT and math.CO
Abstract: 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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