Curious extensions of Ramanujan's ψ11 summation formula

AbstractWe deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan's ψ11 summation and a very-well-poised ψ64 summation as special cases