  Up-down permutations are counted by tangent resp. secant numbers. Considering
words instead, where the letters are produced by independent geometric
distributions, there are several ways of introducing this concept; in the limit
they all coincide with the classical version. In this way, we get some new
q-tangent and q-secant functions. Some of them also have nice continued
fraction expansions; in one particular case, we could not find a proof for it.
Divisibility results a la Andrews/Foata/Gessel are also discussed.
