Abstract :
LetRbe a complete discrete valuation ring with finite residue field, letKbe its quotient field. We construct polynomial functionsphi(n, a)(n=0, 1, …) such that any continuous functionffromRintoKhas the following expansionimagewhere the sequence {an}subset ofKis uniquely determined byfand satisfies thatlimn→∞ an=0. WhenK=Qp, if we replacephi(n,=a) by the binomial coefficienta(a−1)…(a−n+1)/n! we have Mahlerʹs expansion theorem.
