  Periodic point sets model all solid crystalline materials whose structures
are determined in a rigid form and should be studied up to rigid motion or
isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al.
introduced an infinite sequence of density functions that are continuous
isometry invariants of periodic point sets. These density functions turned out
to be highly non-trivial even in dimension 1 for periodic sequences of points
in the line. This paper fully describes the density functions of any periodic
sequence and their symmetry properties. The explicit description theoretically
confirms coincidences of density functions that were previously computed only
through finite samples.
