Abstract. We study summability of formal power series in a variable $t$, whose coefficients are functions of another variable $z$ and are assumed to satisfy certain differential recursion formulas. Such series arise naturally as formal solutions of certain partial differential equations. The results obtained here generalize earlier work for the heat equation by Lutz, Miyake and Schäfke, resp. W. Balser, as well as classical results concerning convergence of formal power series solutions of partial differential equations.

AMS Subject Classification (1991): 35A20, 35A22, 35C10, 35C20

Received January 22, 1999, and in revised form April 21, 1999. (Registered under 2701/2009.)