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math.CA2011
Asymptotic expansions and fast computation of oscillatory Hilbert transforms
Haiyong Wang, Lun Zhang, Daan Huybrechs
In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{iωt})(x)=-int_{0}^{\infty}e^{iωt}\frac{f(t)}…
math.CA2011★ 56 cited
The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
Galina Filipuk, Walter Van Assche, Lun Zhang
We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth…