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Moreover, if in the original system (1) the coefficients of the boundary conditions are polynomials in the parameter, the same is also true when the system is written in the form (2). The systems (1) and (2) are both adapted to a consideration of the associated boundary problems and both of these problems have been discussed under hypotheses of considerable generality.T An essential restriction, however, which has been imposed in all but a few investigations dealing with sys-

The expansion problem in the theory of ordinary linear differential systems of the second order