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October 2018 $q$-series reciprocities and further $\pi$-formulae
Wenchang Chu
Kodai Math. J. 41(3): 512-530 (October 2018). DOI: 10.2996/kmj/1540951251

Abstract

By examining reciprocal relations of basic well-poised, quadratic and cubic series, we establish $q$-analogues of three infinite series for $1/\pi^2$ due to Guillera (2003) and $\lambda$-parameter extensions of three infinite series for $1/\pi$ due to Ramanujan (1914). Several further infinite series identities of Ramanujan-type are also derived as consequences.

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Wenchang Chu. "$q$-series reciprocities and further $\pi$-formulae." Kodai Math. J. 41 (3) 512 - 530, October 2018. https://doi.org/10.2996/kmj/1540951251

Information

Published: October 2018
First available in Project Euclid: 31 October 2018

zbMATH: 07000581
MathSciNet: MR3870701
Digital Object Identifier: 10.2996/kmj/1540951251

Rights: Copyright © 2018 Tokyo Institute of Technology, Department of Mathematics

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Vol.41 • No. 3 • October 2018
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