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- W2071437791 abstract "Let $mu$ be a positive measure on the real line, with associated orthogonal polynomials $left { p_{n}right }$. Let $mbox {Im}aneq 0$. Then there is an explicit constant $c_{n}$ such that for all polynomials $P$ of degree at most $2n-2$, begin{equation*} c_{n}int _{-infty }^{infty }frac {Pleft ( tright ) }{left vert p_{n}left ( aright ) p_{n-1}left ( tright ) -p_{n-1}left ( aright ) p_{n}left ( tright ) right vert ^{2}}dt=int Ptext { }dmu . end{equation*} In this paper, we provide a self-contained proof of this identity. Moreover, we apply the formula to deduce a weak convergence result and a discrepancy estimate, and also to establish a Gauss quadrature associated with $mu$ with nodes at the zeros of $p_{n}left ( aright ) p_{n-1}left ( tright ) -p_{n-1}left ( aright ) p_{n}left ( tright )$." @default.
- W2071437791 created "2016-06-24" @default.
- W2071437791 creator A5014355369 @default.
- W2071437791 date "2010-02-03" @default.
- W2071437791 modified "2023-09-27" @default.
- W2071437791 title "Applications of new Geronimus type identities for real orthogonal polynomials" @default.
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- W2071437791 doi "https://doi.org/10.1090/s0002-9939-10-10276-7" @default.
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