p-adic logarithm
= p-adic logarithm
{c}
{title2=$\log_p$}
The $p$-adic logarithm is the convergent series $\log(1+x)=\sum_{n\geq1}(-1)^{n+1}x^n/n$ on a sufficiently small group of principal units.
It is locally inverse to the <p-adic exponential function>.