= Mahler coefficient exponential generating function
{c}
{title2=$\sum_{n\ge0}c_nT^n/n!=e^{-T}\sum_{n\ge0}f(n)T^n/n!$}
For the <Mahler coefficients> of a <continuous function> on the <p-adic integers>, finite <binomial inversion> gives $c_n=\sum_{j=0}^n(-1)^{n-j}\binom njf(j)$. Equivalently their exponential generating function is the displayed identity in the formal power-series ring $\mathbb Q_p[[T]]$. Each coefficient involves only finitely many terms; no claim of convergence for every $p$-adic value of $T$ is needed.
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