  A master formula of transformation formulas for bilinear sums of basic
hypergeometric series is proposed. It is obtained from the author's previous
results on a transformation formula for Milne's multivariate generalization of
basic hypergeometric series of type $A$ with different dimensions and it can be
considered as a generalization of Whipple-Sears transformation formula for
terminating balanced ${}_4 \phi_3$ series. As an application of the master
formula, one variable cases of some transformation formulas for bilinear sums
of basic hypergeometric series are given as examples. The bilinear
transformation formulas seem to be new in the literature even in one variable
case.
