We present a recursive rule for the symbol of perturbative contributions to the vacuum wave function of a conformally coupled scalar in FRW cosmologies. The rule applies exactly for a class of interactions and cosmologies, which contains λφ 3 in dS 4 , a case of particular relevance as a source of building blocks for inflationary correlators. We use the rule to efficiently reproduce the tree-level four-point contribution and present novel computations of the bubble integrand and the tree-level five-point contribution. Our results apply equally well to the computation of Witten diagrams in Euclidean AdS.

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We need merely show that any solution yj = yj (j = l, • • • , w), in any extension Ji of J, of the form F is a solution of each C*.3 Since this is true if F has no solutions, we may assume that F effectively involves the unknowns. Make the substitution yj = Zj+yj in (1). Let A consist of the terms of F of lowest degree in the Zj and their derivatives. Collecting terms of the same degree, we see that Using the ideas of the above proof together with a uniqueness result of J. F. Ritt, 4 one can very easily prove the following generalization.