no code implementations • 24 Feb 2021 • Xiaojing Chen, Wenchang Chu
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 33D15, 05A30, 11B65, 33D05
