  Let $k$ be a discretely valued non-Archimedean field. We give an explicit
description of analytic functions whose norm is bounded by a given real number
$r$ on tubes of reduced $k$-analytic spaces associated to special formal
schemes (those include $k$-affinoid spaces as well as open polydiscs). As an
application we study the connectedness of these tubes. This generalizes (in the
discretely valued case) a result of Siegfried Bosch. We use as a main tool a
result of A.J. de Jong relating formal and analytic functions on special formal
schemes and a generalization of de Jong's result which is proved in the joint
appendix with Christian Kappen.
