q-series reciprocities and further π-formulae

Wenchang Chu

doi:10.2996/kmj/1540951251

Kodai Mathematical Journal

Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991

q-series reciprocities and further π-formulae

Wenchang Chu

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Keywords: Infinite series of Ramanujan-type, Well-poised series, Quadratic series, Cubic series, Reciprocal relation of q-series

JOURNAL FREE ACCESS

2018 Volume 41 Issue 3 Pages 512-530

DOI https://doi.org/10.2996/kmj/1540951251

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Abstract

By examining reciprocal relations of basic well-poised, quadratic and cubic series, we establish q-analogues of three infinite series for 1/π² due to Guillera (2003) and λ-parameter extensions of three infinite series for 1/π due to Ramanujan (1914). Several further infinite series identities of Ramanujan-type are also derived as consequences.

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