  We study the one-dimensional asymmetric simple exclusion process (ASEP) with
open boundary conditions. Particles are injected and ejected at both
boundaries. It is clarified that the steady state of the model is intimately
related to the Askey-Wilson polynomials. The partition function and the
$n$-point functions are obtained in the integral form with four boundary
parameters. The thermodynamic current is evaluated to confirm the conjectured
phase diagram.
