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arXiv · 2102.12440

$q$-Analogues of $π$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{ü}tz Theorem

Xiaojing Chen·Wenchang Chu
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Abstract

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

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Xiaojing Chen, Wenchang Chu. 2021-02-24. $q$-Analogues of $π$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{ü}tz Theorem. https://arxiv.org/abs/2102.12440

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