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

Transformation formulas for bilinear sums of basic hypergeometric series