Transformation formula for a double Clausenian hypergeometric series, its \(q\)-analogue, and its invariance group (Q5957969)

In the notions of \textit{H. M. Srivastava} and \textit{P. W. Karlsson} [Multiple Gaussian hypergeometric series (1985; Zbl 0552.33001)] for generalized basic double series \(\varphi^{1,2,2}_{0,2,2}\), the author works out an useful transformation formula for a terminating \(\varphi^{1,2,2,}_{0, 2,2}\) series, giving rise to a transformation (invariance) group. Special cases of the result obtained here provide interesting known results.