Abstract
We give q-analogues of three Ramanujan-type series for \(1/\pi \) from q-analogues of ordinary WZ pairs. The first one is a new q-analogue of the following Ramanujan’s formula for \(1/\pi \):
of which another q-analogue was given by the author and Liu early and reproved by different authors. We also present a WZ proof of a q-analogue of Bauer’s (Ramanujan-type) formula and discuss some related congruences and q-congruences.
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Notes
Doron Zeilberger’s computer servant.
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The author would like to thank the anonymous referee for helpful comments on a previous version of this paper.
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This work was partially supported by the National Natural Science Foundation of China (Grant 11771175)
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Guo, V.J.W. q-Analogues of three Ramanujan-type formulas for \(1/\pi \). Ramanujan J 52, 123–132 (2020). https://doi.org/10.1007/s11139-018-0096-6
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DOI: https://doi.org/10.1007/s11139-018-0096-6