On some orthogonal polynomials of interest in theoretical chemistry
- Walter Gautschi
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Constructive methods are developed for a class of polynomials orthogonal on two symmetric intervals. An analysis is given of certain phenomena of instability in connection with nonlinear recursions. Special cases arising in the study of the diatomic linear chain are worked out explicitly. In one of these cases the associatedn-point Gauss-Christoffel quadrature formula has equal weights whenevern is even.
- G. I. Barkov,On some systems of polynomials orthogonal on two symmetric intervals (Russian), Izv. Vysš. Učebn. Zav. Mat. 1960, No. 4 (17), 3–16.
- T. S. Chihara,An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
- W. Gautschi,Advances in Chebyshev quadrature, in: “Numerical Analysis” (G. A. Watson, ed.), Proc. Dundee Conf. on Numerical Analysis, 1975. Lecture Notes in Mathematics, vol. 506, 1976, pp. 100–121. Springer-Verlag, Berlin, 1976.
- W. Gautschi,Minimal solutions of three-term recurrence relations and orthogonal polynomials, Math. Comp. 36 (1981), 547–554.
- W. Gautschi,An algorithmic implementation of the generalized Christoffel theorem, in: “Numerische Integration” (G. Hämmerlin, ed.), pp. 89–106. Intern. Ser. Numer. Math. 57, Birkhäuser, Basel, 1982.
- W. Gautschi,On generating orthogonal polynomials, SIAM J. Sci. Stat. Comput. 3 (1982), 289–317.
- Ja. L. Geronimus,On the Chebyshev quadrature formula (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1182–1207. [English translation in: Math. USSR-Izv. 3 (1969), 1115–1138].
- G. H. Golub and J. Kautsky,Calculation of Gauss quadratures with multiple free and fixed knots, Numer. Math. 41 (1983), 147–163.
- I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products, Academic Press, New York, 1965.
- J. Kautsky and G. H. Golub,On the calculation of Jacobi matrices, Linear Algebra Appl. 52/53 (1983), 439–455.
- C. Posse,Sur les quadratures, Nouv. Ann. Math. (2) 14 (1975), 49–62.
- G. Szegö,Orthogonal Polynomials, 4th ed., AMS Colloquium Publications 23, American Mathematical Society, Providence, R.I., 1975.
- J. C. Wheeler,Modified moments and continued fraction coefficients for the diatomic linear chain, J. Chem. Phys. 80 (1984), 472–476.
- On some orthogonal polynomials of interest in theoretical chemistry
BIT Numerical Mathematics
Volume 24, Issue 4 , pp 473-483
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Industry Sectors
- Walter Gautschi (1)
- Author Affiliations
- 1. Purdue University, Mathematical Sciences Building, Room 442, 47907, West Lafayette, Indiana, USA