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- W2011569082 abstract "We discuss the asymptotic behavior (as n→∞) of the entropic integralsEn=-∫-11logpn2(x)pn2(x)w(x)dx,andFn=-∫-11logpn2(x)w(x)pn2(x)w(x)dx,when w is the symmetric Pollaczek weight on [-1,1] with main parameter λ⩾1, and pn is the corresponding orthonormal polynomial of degree n. It is well-known that w does not belong to the Szegő class, which implies in particular that En→-∞. For that sequence we find the first two terms of the asymptotic expansion. Furthermore, we show that Fn→log(π)-1, proving that this “universal behavior” extends beyond the Szegő class. The asymptotics of En has also a curious interpretation in terms of the mutual energy of two relevant sequences of measures associated with pn's." @default.
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- W2011569082 date "2007-03-01" @default.
- W2011569082 modified "2023-09-27" @default.
- W2011569082 title "Shannon entropy of symmetric Pollaczek polynomials" @default.
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- W2011569082 doi "https://doi.org/10.1016/j.jat.2006.06.007" @default.
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