  In 1981, Andrews gave a four-variable generalization of Ramanujan's
${_1\psi_1}$ summation formula. We establish a six-variable generalization of
Andrews' identity according to the transformation formula for two ${_8\phi_7}$
series and Bailey's transformation formula for three ${_8\phi_7}$ series. Then
it is used to find a six-variable generalization of Ramanujan's reciprocity
theorem, which is different from Liu's formula. We derive the generalizations
of Bailey's two $_3\psi_3$ summation formulas in terms of two limiting
relations and Bailey's another transformation formula for three $_8\phi_7$
series. Based on the two limiting relations, some different results involving
bilateral basic hypergeometric series are also deduced from the Guo--Schlosser
transformation formula and other two transformation formulas.
