Characterization of connection coefficients for hypergeometric systems (Q1105089)

Starting from the fact that the equation (1) \((I-B)dX/dt=AX\), where X is a an n-dimensional column vector, \(B=diag[\lambda_ 1,\lambda_ 2,...,\lambda_ n]\), \(A\in M_ n(C)\), can be solved by the intermediate of the system of linear differential equations (2) \((B- \lambda)(z+1)G(z+1)=(z-A)G(z),\) the paper deals with a complete solution of (1), when A is diagonalizable and has only two eigenvalues. Power series solutions of (1) near singularities are studied and Barnes integral representations of solutions are presented.