Numerical integration using rys polynomials

Harry F. King, Michel Dupuis

Research output: Contribution to journalArticlepeer-review

212 Citations (Scopus)


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 languageEnglish
Pages (from-to)144-165
Number of pages22
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 1976

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

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