Holonomic \(q\)-difference system associated with the basic hypergeometric series \(_{n+1}\varphi_ n\) (Q1319189)

The author derives the holonomic \(q\)-difference system with respect to the variable \(z\), which is associated with the Jackson integral which is one of the integral representations of the basic hypergometric function \(_{n+1} \varphi_ n\). The cases \(n=1\) and \(n=2\) are considered. The second result of the paper is the determinant formula. The calculation of the determinant of the coefficient matrix \(A\) of the derived system leads to the \(q\)-difference equation for the Wronskian. The author gives an expression for the Wronskian near the origin \(z=0\) and the infinity \(z=\infty\). The connection coefficients between them are also given.