  By a codimension-one system we mean a system whose lattice of relations has
rank one. We consider codimension-one $A$-hypergeometric systems and explicitly
construct some of the logarithmic series solutions at the origin. When the
parameter vector $\beta$ is nonresonant we obtain a full set of logarithmic
series solutions at the origin by this procedure. We also determine when a
codimension-one system with nonresonant parameter can have maximal unipotent
monodromy at the origin.
