, Volume 24, Issue 4, pp 473-483

On some orthogonal polynomials of interest in theoretical chemistry

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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.

To Germund Dahlquist on his 60th birthday
Research supported in part by the National Science Foundation under grant MCS-7927158A1.