Asymptotics of recurrence coefficients for orthonormal polynomials on the line—Magnus’s method revisited

Damelin, S.

doi:10.1090/S0025-5718-03-01553-9

Asymptotics of recurrence coefficients for orthonormal polynomials on the line—Magnus’s method revisited
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by S. B. Damelin PDF

Math. Comp. 73 (2004), 191-209 Request permission

Abstract:

We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials $p_n(w^2)$ for weights $w=W\exp (-Q)$ on the real line where $Q$ is an even polynomial of fixed degree with nonnegative coefficients or where $Q(x) =\exp (x^{2m}), m\geq 1$. Here $W(x)=|x|^{\rho }$ for some real $\rho >-1$.

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