Statement
Suppose U is an open set in the Euclidean space Rn, and suppose that f0, f1 ... is a sequence of smooth, complex-valued functions on U. If I is an any open interval in R containing 0 (possibly I = R), then there exists a complex-valued smooth function F(t, x) defined on I×U, such that
for k ≥ 0 and x in U.
Read more about this topic: Borel's Lemma
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