  An earlier contour expression for the Green function of a free complex scalar
field in the presence of a conical singularity with localised magnetic flux is
shown to yield expressions for the field correlator and defect block expansions
that have been more recently found in connection with monodromy defects in
conformal field theory. The Green function appears as the Picard integral
representation of the Appell $F_1$ function. This is shown to transform into a
confluent Horn function, corresponding to a different defect block expansion.
Other transformations are discussed.
