The \((f,g)\)-inversion formula and its applications: the \((f,g)\)-summation formula (Q2643868)

The author introduced a characterization of the two functions \(f(x,y)\) and \(g(x,y)\) in the \((f,g)\)-inversion. He unified the bibasic summation formulas of Gasper and Rahman, Chu, and Macdonald. Furthermore, he obtained an alternative proof of the \((f,g)\)-inversion by the \((f,g)\)-summation formula and a bilateral \((f,g)\)-inversion containing Schlosser's bilateral matrix inversion as a special case.