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The boundary value and expansion problems for the equation of the nth order with boundary conditions at two points have been studied by Birkhoff.t Bochert has suggested the generalization of these results to the equation with auxiliary conditions at more than two points. Such generalization of the essential properties of the differential system has been carried out by the author, and in this paper is given the proof of the convergence of the expansion, which may be studied quite independently of the other results. The formal development of the boundary problem and a more detailed discussion of the form of the series will be presented in other papers. The differential equation is taken in the form

Expansion problems of ordinary linear differential equations with auxiliary conditions at more than two points