H. Karabulut et El. Sibert, DISTRIBUTED GAUSSIAN POLYNOMIALS AND ASSOCIATED GAUSSIAN QUADRATURES, Journal of mathematical physics, 38(9), 1997, pp. 4815-4831
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.