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Values of the $p$-adic exponential function at integers
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Numbers
$p$
$k$
$\exp_p(k)$
INPUT{numbers.yaml} (not shown in preview)
Definition
This table constains values $\exp_p(k) \in \mathbb{Z}_p$ of the $p$-adic exponential function at certain integers $k$.
Parameters
$p$
—   integer (prime)
$k$
—   integer ($|k|_p < p^{-1/(p-1)}$)
The $p$-adic logarithm is defined by its Taylor series for all $x \in \mathbb{C}_p$ within the radius of convergence, $|x|_p < p^{-1/(p-1)}$.