  The equation of state of Quantum Chromodynamics (QCD) at finite density is
currently known only in a limited range in the baryon chemical potential
$\mu_B$. This is due to fundamental shortcomings of traditional methods such as
Taylor expansion around $\mu_B=0$. In this contribution, we present an
alternative scheme that displays substantially improved convergence over the
Taylor expansion method. We calculate the alternative expansion coefficients in
the continuum, and show our results for the thermodynamic observables up to
$\mu_B/T\le3.5$.
