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Presented to the Society, November 26, 1943; received by the editors November 13, 1943. This paper was prepared while the author was a fellow under the Program of Advanced Instruction in Mechanics at Brown University. 1 S. Bergman, (a) Zur Theorie der Funktionen, die eine linear e partielle Differentialgleichung befriedigen, Rec. Math. (Mat. Sbornik) N.S. vol. 44 (1937) pp. 1169-1198; (b) The approximation of functions satisfying a linear partial differential equation, Duke Math. J. vol. 6 (1940) pp. 537-561; (c) Linear operators in the theory of partial differential equations, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 130-155; (d) On the solutions of partial differential equations of the fourth order, to appear later.

A recurrence formula for the solutions of certain linear partial differential equations