DISTRIBUTED GAUSSIAN POLYNOMIALS AND ASSOCIATED GAUSSIAN QUADRATURES

An orthogonal function set called distributed Gaussian orthogonal poly nomials is constructed from equally spaced Gaussians and the correspon ding quadrature is studied. The infinite chain limit of both polynomia ls and the quadrature is studied and analytical expressions are found for polynomials, quadrature points, weights, and Lagrange functions. T he connections to Wannier functions are explored, and a way of constru cting Wannier functions from Gaussians is proposed. (C) 1997 American Institute of Physics.