  We study the ground-state properties and excitation spectrum of the
Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact
interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by
using an analytic method based on a series expansion on orthogonal polynomials
developed in \cite{Ristivojevic} and push the expansion to an unprecedented
order. By a careful analysis of the mathematical structure of the series
expansion, we make a conjecture for the analytic exact result at zero
temperature and show that the partially resummed expressions thereby obtained
compete with accurate numerical calculations. This allows us to evaluate the
density of quasi-momenta, the ground-state energy, the local two-body
correlation function and Tan's contact. Then, we study the two branches of the
excitation spectrum. Using a general analysis of their properties and
symmetries, we obtain novel analytical expressions at arbitrary interaction
strength which are found to be extremely accurate in a wide range of
intermediate to strong interactions.
