  Special coordinate systems are constructed in a neighborhood of a point or of
a curve. Taylor expansions can then be easily inferred for the metric, the
connection, or the Finsler Lagrangian in terms of curvature invariants. These
coordinates circumvent the difficulties of the normal and Fermi coordinates in
Finsler geometry, which in general are not sufficiently differentiable. They
are obtained applying the usual constructions to the pullback of a horizontally
torsionless connection. The results so obtained are easily specialized to the
Berwald or Chern-Rund connections and have application in the study of the
equivalence principle in Finslerian extensions of general relativity.
