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is /(/)=s=0. This may be seen by observing that none of the fundamental solutions of equation (1), t (w=—fe, — fe+1, • • • > ft —2), satisfies the boundary conditions (2). We now replace equation (1) by another of infinite order, retaining the boundary conditions (2), and investigate the possibility of a nonvanishing solution. We let k become infinite in equation (1) after introduction of a factor. Set

A homogeneous differential system of infinite order with nonvanishing solution