An analog of Szegö’s formula for asymptotic Töeplitz determinants is proved for Hankel determinants. The proof uses a set of recurrence formulas developed for polynomials orthogonal on a finite segment of the real line and some properties of the Jost function associated with those polynomials. The techniques of inverse scattering theory are used to calculate the correction terms to the asymptotic formula. The results are valid for weight functions that have a finite number of jump points and an absolutely continuous part that is unbounded.
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Jeffrey S. Geronimo (1979) studied this question.
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