Continuous functions on discrete valuation rings

Let R be a complete discrete valuation ring with finite residue field, let K be its quotient field. We construct polynomial functions phi(n, a)(n = 0, 1,...) such that any continuous Function f from R into K has the following expansion [GRAPHICS] where the sequence {a(n)} subset of K is uniquely determined by J and satisfies that lim(n --> infinity) a(n) = 0. When K = Q(p), if we replace phi(n,a) by the binomial coefficient a(a - 1) ... (a - n + 1)/n! we have Mahler's expansion theorem. (C) 1999 Academic Press.