q-series reciprocities and further π-formulae

抄録

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.