We give an elementary proof of holonomicity for
-hypergeometric
systems, with no requirements on the behavior of their singularities, a result
originally due to Adolphson (1994) after the regular singular case by
Gelfand and Gelfand (1986). Our method yields a direct de novo proof that
-hypergeometric
systems form holonomic families over their parameter spaces, as shown by
Matusevich, Miller, and Walther (2005).