  The harmonic sum of the integers which are missing $p$ given digits in a base
$b$ is expressed as $b\log(b)/p$ plus corrections indexed by the excluded
digits and expressed as integrals involving the digamma function and a suitable
measure. A number of consequences are derived, such as explicit bounds,
monotony, series representations and asymptotic expansions involving the zeta
values at integers, and suitable moments of the measure. In the classic Kempner
case of $b=10$ and $9$ as the only excluded digit, the series representation
turns out to be exactly identical with a result obtained by Fischer already in
1993. Extending this work is indeed the goal of the present contribution.
