  We develop a moment method based on the Hermite series of arbitrary order to
calculate viscous-slip, thermal-slip, and temperature-jump coefficients for
general gas-surface scattering kernels. Under some usual assumptions of
scattering kernels, the solvability is obtained by showing the positive
definiteness of the symmetric coefficient matrix in the boundary conditions.
For gas flows with the Cercignani-Lampis gas-surface interaction and
inverse-power-law intermolecular potentials, the model can capture the slip and
jump coefficients accurately with elegant analytic expressions. On the one
hand, the proposed method can apply to the cases of arbitrary order moments
with increasing accuracy. On the other hand, the explicit formulae for
low-order situations are simpler and more accurate than some existing results
in references. Therefore, one may apply these formulae in slip and jump
conditions to improve the accuracy of macroscopic fluid dynamic models for gas
flows.
