Explicit orthogonal polynomials for reciprocal polynomial weights on (-∞,∞)

Lubinsky, D.

doi:10.1090/S0002-9939-08-09754-2

Explicit orthogonal polynomials for reciprocal polynomial weights on $(-\infty ,\infty )$
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by D. S. Lubinsky PDF

Proc. Amer. Math. Soc. 137 (2009), 2317-2327 Request permission

Abstract:

Let $S$ be a polynomial of degree $2n+2$, that is, positive on the real axis, and let $w=1/S$ on $(-\infty ,\infty )$. We present an explicit formula for the $n$th orthogonal polynomial and related quantities for the weight $w$. This is an analogue for the real line of the classical Bernstein-Szegő formula for $\left (-1,1\right )$.

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