Mathematics, Department of


Date of this Version



Published in Bull. Amer. Math. Soc. 37 (1931) 439-446.


C. C. Camp has shown the convergence of the expansion of an arbitrary function in terms of the solutions of the systems of equations
X1’a1 - Σi=2nμi)X1 = 0,
X1’ai + μi)Xi = 0, (j = 2, 3, …, n),
where the ai’s are functions of x, with the boundary conditions
Xi(-π) = Xi(π), (j = 1, 2, …, n).
In this paper it is intended to use a differential system in which the n parameters appear in each equation with a function ajk(xj) multiplying each. The boundary conditions will also be more general.

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