  We develop a generalized harmonic-fluid approach, based on a regularization
of the effective low-energy Luttinger-liquid Hamiltonian, for a one-dimensional
Bose gas with repulsive contact interactions. The method enables us to compute
the complete series corresponding to the large-distance, off-diagonal behavior
of the one-body density matrix for any value of the Luttinger parameter K. We
compare our results with the exact ones known in the Tonks-Girardeau limit of
infinitely large interactions (corresponding to K=1) and, different from the
usual harmonic-fluid approach, we recover the full structure of the series. The
structure is conserved for arbitrary values of the interaction strength, with
power laws fixed by the universal parameter K and a sequence of subleading
corrections.
