Abstract
We define and discuss the properties of manifolds of polynomials Jn(t, x) and Rn(t, x), called Rys polynomials, which are orthonormal with respect to the weighting factor exp(-xt2) on a finite interval of t. Numerical quadrature based on Rys polynomials provides an alternative approach to the computation of integrals commonly encountered in molecular quantum mechanics. This gives rise to a curve fitting problem for the roots and quadrature weights as a function of the x parameter. We have used Chebyshev approximation for small x and an asymptotic expansion for large x. A modified Christoffel-Darboux equation applicable to Rys polynomials is derived and used to obtain alternative formulas for Rys quadrature weight factors.
Original language | English |
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Pages (from-to) | 144-165 |
Number of pages | 22 |
Journal | Journal of Computational Physics |
Volume | 21 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1976 |
ASJC Scopus subject areas
- Computer Science Applications
- Physics and Astronomy(all)