  We discuss approximate formulas for the dynamic structure factor of the
one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable
over a wide range of the relevant parameters such as the interaction strength,
frequency, and wavenumber. The suggested approximations are consistent with the
exact results known in limiting cases. In particular, we encompass exact edge
exponents as well as Luttinger liquid and perturbation theoretic results. We
further discuss derived approximations for the static structure factor and the
pair distribution function g(x). The approximate expressions show excellent
agreement with numerical results based on the algebraic Bethe ansatz.
