  A lattice Boltzmann method is proposed based on the expansion of the
equilibrium distribution function in powers of a new set of generalized
orthonormal polynomials which are here presented. The new polynomials are
orthonormal under the weight defined by the equilibrium distribution function
itself. The D-dimensional Hermite polynomials is a sub-case of the present
ones, associated to the particular weight of a gaussian function. The proposed
lattice Boltzmann method allows for the treatment of semi-classical fluids,
such as electrons in metals under the Drude-Sommerfeld model, which is a
particular case that we develop and validate by the Riemann problem.
