p-adic logarithm (source code)

= p-adic logarithm
{title2=$\log_p$}
{wiki=P-adic_exponential_function}

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.